This article about the Uvedale family by Granville Leveson Gower, from Surrey Archaeological Collections, Vol 3., 1865, might be the source Richardson has used to obtain information about Sir Thomas Uvedale.
Information about Sir Thomas starts on page 90, and apparently there were 2 sons named William (both surviving their father). His will in latin, and translation starts on p. 158 (Appendix V) and the dates agree with what is currently on the WikiTree profile.