Dugdale, in The Antiquities of Warwickshire, volume 1, page 400 has an image of the 10 daughters of Sir Thomas de Beauchamp and his wife Katherine taken from South windows of the quire (choir?) in Collegiate Church of St Mary's, Warwick, and there is an Agneta (Agnes) but no Anne. However much of the Church was destroyed in a fire in 1693, so it's not clear if the etchings of the windows depicting the daughters were from before 1693 or the windows were added after that date when the church was rebuilt?
On page 399, second column of the same book, Dugdale mentions presumed sons John and Hierome again based on images on glass presumably with the surcoat of arms of the Beauchamps, but Dugdale isn't convinced and states that they aren't named in the Rous Roll
On the same page he does mention two illegitimate children of Sir Thomas, a son, Sir John Addurston, Knight, and a daughter Mary, the wife of Sir Richard Herthull, Knight, who from the footnotes are named in the Rous Roll I think.
No mention of a son Richard anywhere that I can see.