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Edit 1. All the books that I found which deal with numerical estimates of literacy in late medieval and early modern times favor the ability to sign as an estimator of the degree of literacy. In addition to Houston's book (whose book has the entire chapter comparing different methods, including ones which I find rather exotic, such as materials of Spanish Inquisition trials):

The authors analyze other available methods, note merits and demerits of each and, in the end, conclude in favor of signage.

Jo Ann Hoeppner Moran. "Literacy and Education in Northern England, 1350-1530: A Methodological Inquiry." Northern History, 17 (1981): 1-23

Moran's article is the only one that I found which provides numerical estimates of literacy in England in 13-15th centuries. She notes, however, lack of extant records and bases her estimates on availability of schooling (making the numbers less reliable, at least according to O'Day). I will add info with her numbers when I have more time.

From reading Cressy's book, I think, I found the original source of the claim that about half of English population by the end of 15th century was literate. He attributes the number to Thomas More:

I am unsure where the claim that (generically) women were prohibited from "signing anything" comes from. As fas as early modern England goes, it is plain wrong. For instance Cressy documents striking difference in signage among women in London and elsewhere by the late 17th century: The percentage for both categories started near zero in 1500 and increased only to about 20% outside of London by the late 17th century. At the same time, in London, it reached about 50% by late 17th century. As far as I can tell, this dynamics completely invalidates the conjecture that women were prohibited from signing their names.

Edit 2. Regarding Mark Olson's request: While Cressy's book contains mass of numerical data related to literacy (based on various archival work), it is all broken into subcategories according to occupation and geography and, in the book, I could not find aggregate overall numbers. But, in his later paper, from 1993, "Literacy in context: meaning and measurement in early modern England", Cressy writes:

Thus, according to this estimate, the rate of literacy in mid-16th century England was about 12.5%. This makes Houston's estimate of 10% at the year of 1500 quite reasonable.

Edit 1. Regarding Mark Olson's request, below are estimates of literacy at the end of the medieval times/early modern times from other authors.

All the books that I found which deal with numerical estimates of literacy in late medieval and early modern times favor the ability to sign as an estimator of the degree of literacy. In addition to Houston's book (whose book has the entire chapter comparing different methods, including ones which I find rather exotic, such as materials of Spanish Inquisition trials):

Adam Fox, "Oral and Literate Culture in England, 1500–1700." Oxford University Press, 2000.

Jo Ann Hoeppner Moran. "Literacy and Education in Northern England, 1350-1530: A Methodological Inquiry." Northern History, 17 (1981): 1-23.

Moran's article is the only one that I found which provides numerical estimates of literacy in England in 13-15th centuries. She notes, however, lack of extant records and bases her estimates on availability of schooling (making the numbers less reliable, at least according to O'Day).

Some of Moran's research results are summarized by O'Day as follows:

From this source [availability of schooling] she concludes that some 15% of the population of York diocese attended a school in the late 15th century, as compared with perhaps 9% in the early 15th century and some 4.7% in the late 14th century. But it may be suspected that these figures err considerably on the generous side. Dr. Moran based these estimates on calculations which assumed a regular and constant size for the schools concerned. Later evidence suggests that consistency in this respect was not a feature of early schools.

From reading Cressy's book, I think, I found the original source of the claim that about half of English population by the end of 15th century was literate. He attributes the number to Thomas More:

While Cressy's book contains mass of numerical data related to literacy (based on various archival work), it is all broken into subcategories according to occupation and geography and, in the book, I could not find aggregate overall numbers. But, in his later paper, from 1993, "Literacy in context: meaning and measurement in early modern England", Cressy writes:

Thus, according to this estimate, the rate of literacy in mid-16th century England was about 12.5%.

Another estimate (dealing with the end of the medieval time and, thus, closer to the OP), based on the signage records appears in

Adam Fox, "Oral and Literate Culture in England, 1500–1700." Oxford University Press, 2000.

Based on the early arguments from Schofields 1973 article (which is widely cited and described as the breakthrough leading to transition from qualitative to quantitative estimates in literacy during early modern times), Fox then estimates that these numbers should be doubled to get an estimate of the reading capacity, thus, getting:

10% adult male reading and 2% adult female reading in England in 1500.

Lastly, regarding criticisms of usage of signage as a mean of estimating rates of literacy (ability to read) in late medieval/early modern times:

1. In their books O'Day, Cressy and Houston analyze in detail other available methods, note merits and demerits of each and, in the end, conclude in favor of signage. (This again follows Schofield's 1973 article.) In particular, they do discuss arguments similar to the one in Adam Baker's comment below, suggesting that for some people signing with a symbol/picture instead of the written name was a choice rather than the result of illiteracy. Reproducing these arguments here would take too much space and my answer is already too long, so I will refrain from doing so.

2. I am unsure about the origin of the claim that (generically) women were prohibited from "signing anything." I do not exclude that this was indeed the case in some places and at certain times. However, as fas as late medieval/early modern England goes, the claim is plain wrong. For instance Cressy documents striking difference in signage among women in London and elsewhere by the late 17th century: The percentage for both categories started near zero in 1500 and increased only to about 20% outside of London by the late 17th century. At the same time, in London, it reached about 50% by late 17th century. As far as I can tell, this dynamics completely invalidates the conjecture that women (at least in the discussed time period) were prohibited from signing their names.

Ditto the numbers provided by Houston in his article and the book for other parts of Europe: They indicate slow (but uneven) growth of female literacy (as measured by name signage) elsewhere in Europe, indicative of improvement of education rather than abolishing of some laws prohibiting signage.

Edit. All the books that I found which deal with numerical estimates of literacy in late medieval and early modern times favor the ability to sign as an estimator of the degree of literacy. In addition to Houston's book (whose book has the entire chapter comparing different methods, including ones which I find rather exotic, such as materials of Spanish Inquisition trials):

O'Day characterizes as "wildly optimistic" the estimates of 30% literacy in the late 15th century.

I am unsure where the claim that (generically) women were prohibited from "signing anything" comes from. As fas as early modern England goes, it is plain wrong. For instance Cressy documents striking difference in signage among women in London and elsewhere by the late 17th century: The percentage for both categories started near zero in 1500 and increased only to about 20% outside of London by the late 17th century. At the same time, in London, it reached about 50% by late 17th century. As far as I can tell, this dynamics completely invalidates the conjecture that women were prohibited from signing their names.

Edit 1. All the books that I found which deal with numerical estimates of literacy in late medieval and early modern times favor the ability to sign as an estimator of the degree of literacy. In addition to Houston's book (whose book has the entire chapter comparing different methods, including ones which I find rather exotic, such as materials of Spanish Inquisition trials):

O'Day characterizes as "wildly optimistic" the estimates of 30% literacy in the late 15th century.

Moran's article is the only one that I found which provides numerical estimates of literacy in England in 13-15th centuries. She notes, however, lack of extant records and bases her estimates on availability of schooling (making the numbers less reliable, at least according to O'Day). I will add info with her numbers when I have more time.

I am unsure where the claim that (generically) women were prohibited from "signing anything" comes from. As fas as early modern England goes, it is plain wrong. For instance Cressy documents striking difference in signage among women in London and elsewhere by the late 17th century: The percentage for both categories started near zero in 1500 and increased only to about 20% outside of London by the late 17th century. At the same time, in London, it reached about 50% by late 17th century. As far as I can tell, this dynamics completely invalidates the conjecture that women were prohibited from signing their names.

Edit 2. Regarding Mark Olson's request: While Cressy's book contains mass of numerical data related to literacy (based on various archival work), it is all broken into subcategories according to occupation and geography and, in the book, I could not find aggregate overall numbers. But, in his later paper, from 1993, "Literacy in context: meaning and measurement in early modern England", Cressy writes:

Thus, according to this estimate, the rate of literacy in mid-16th century England was about 12.5%. This makes Houston's estimate of 10% at the year of 1500 quite reasonable.

I am unsure what the claim that (generically) women were prohibited from "signing anything" comes from. As fas as early modern England goes, it is plain wrong. For instance Cressy documents striking difference in the percentage of women in London and elsewhere by the late 17th century: The percentage for both categories started near zero in 1500 and increased only to about 20% outside of London by the late 17th century. At the same time, in London, it reached about 50% by late 17th century. As far as I can tell, this dynamics completely invalidates the conjecture that women were prohibited signing their names.

I am unsure where the claim that (generically) women were prohibited from "signing anything" comes from. As fas as early modern England goes, it is plain wrong. For instance Cressy documents striking difference in signage among women in London and elsewhere by the late 17th century: The percentage for both categories started near zero in 1500 and increased only to about 20% outside of London by the late 17th century. At the same time, in London, it reached about 50% by late 17th century. As far as I can tell, this dynamics completely invalidates the conjecture that women were prohibited from signing their names.