If a Jewish family settled in 15th century London, would they be reported to the mayor or another authority? Did any Jewish families resist the 13th century expulsion?
Are there any mentions of Jews in England at all between 1290 and 1657?
There were those that stayed. The records of the Domus Conversorum tells us this. However out side of those records, little is available from the era immediately after the expulsion. Occasional permits would allow for individual jews to come and an accusation against traders that they were jewish, and not lombards as they claimed, occurred in 1376. In the Elizabethan Era, Jews were known to exist in London however they claimed to be converts. Rodrigo Lopez, a shephardic jew, was executed by Queen Elizabeth. Since Judaism was outlawed, little record exists from the era of exclusion, but it is safe to say there were at least some Jews in England during the period.
I heard that the Bassano family of musicians from Venice were Jewish. http://en.m.wikipedia.org/wiki/Jeronimo_Bassano I know the wiki link disputes that claim but I heard it nonetheless.