He succeeded his elder brother Sir Walter Wrottesley as baronet in 1732.[4]
It is said that when Bonnie Prince Charlie was marching south through England during the course of his rebellion, Sir Richard, a regular duellist, armed his tenants and gathered his servants to do battle but he reportedly never got further than a local inn, The Bull at Codsall, where his small team of men spent a convivial week.[5]
He became M.P. for Tavistock in December 1747, holding the seat until 1754. He was appointed a Clerk of the Green Cloth from 1749 to 1754.
He became a Church official, being appointed minister of St Michael's in Tettenhall.[5] He was appointed chaplain in ordinary to the King, George III, in 1763 and collated Dean of Worcester for life in 1765.