After manager Steve Lovell's resignation in November that year, United surprised many by bringing in ex-Wales and Everton goalkeeper Neville Southall, and with him came an upturn in fortunes, with eventually United consolidating their position in their new league.
During this period, in the late 1970s, the club also reached the quarter finals of the FA Trophy and featured future Welsh international goalkeeper Neville Southall.
Neville Chamberlain | Richard Neville, 16th Earl of Warwick | Aaron Neville | The Neville Brothers | Southall | Neville Symington | Neville Brody | Gary Neville | Cynthia Neville | John Neville, 1st Marquess of Montagu | Ivan Neville | Neville | Katherine Neville | Neville Wran | Neville Southall | Neville Duke | Neville Cardus | Katherine Neville, Baroness Hastings | Katherine Neville (author) | John Neville | House of Neville | Stuart Neville | Ralph Neville, 2nd Baron Neville de Raby | Ralph de Neville, 1st Earl of Westmorland | Neville Hiscock | Neville Brand | John Neville (actor) | Edgar Neville | Charles Neville (musician) | Charles Neville |
However, the then 23-year old was unable to displace established Everton goalkeeper Neville Southall, and his only appearances in the 1987–88 season were during a loan spell at Tranmere.
However, due to an injury to Neville Southall, Mimms played in goal for Everton for a large part of the 1985–86 season.