The number of knights in England between 1324 and 1436 turns out to be a difficult question to answer, because it changed greatly over time.
In 1324, there was a major effort to determine how many knights were available for military service in England. Unfortunately, some county reports have been lost, and some knights with holdings in more than one county were counted more than once. About 1,200 knights seems to be a fair estimate based on that evidence.
In 1436 there was a lay subsidy that attempted to count lay land holders with lands with more than five pounds a year in rental value. This should have captured most of the individuals wealthy enough to be a knight. The number of knights recorded were about a seventh of the 1324 number when like counties can be compared.
In the army that Edward III sent to besiege Calais in 1346-47, about a fifth of the men-at-arms were knights. When Henry V sent an army to besiege Harfleur in 1415, the knights had shrunk to about 7% of the total number of men-at-arms.
Knights in 14th and 15th c. England were expected to perform burdensome unpaid duties in local government. In the early 14th c., the crown worked to provide positive incentives to counteract that burden. In 1306 at the Feast of the Swans, Edward I offered to provide all the necessary military and ceremonial equipment to all presenting themselves to be knighted. Later, the government apparently concluded that the rank of knighthood was a less important measure of military strength than the number of men having the equipment required to serve as a man-at-arms. With reduced incentives to serve, the number of knights shrank.
The numbers of named knights cited above could be high or low. A father and son that served in the same decade could be counted as two different names, even though the number of knights who served in any given year could have been one or less. And some knights must have been uncaptured by any historical record.