The club changed its name to ″London Cornish″ shortly thereafter and played occasional fixtures in a variety of locations until moving to the current ground, the Richardson Evans Memorial Playing Fields just off the A3 and home to the Harlequins RFC Training Ground, in 1972. These grounds have been rented to the club every season since that year by Wimbledon and Putney Common Conservators. A conservators' rule currently exists that forbids any matches kicking off later than 14:15 on a Saturday.
The advent of the League system saw London Cornish join the Middlesex division and there they stayed until the season of 1997–98 when the club transferred to Surrey 3. After one season in the new league, London Cornish saw vast improvement year on year, achieving four promotions in seven years. They are now competing for promotion from London 2 South West. London Cornish have four, and sometimes five XVs.
The current Director of Rugby and Head Coach, Redruth born Dickon Moon, took on the role at the start of 2003–04, having joined the club from Old Patesians RFC.