The Garden County trailed early in the second half, but kicked six points in a 13-minute purple patch to keep their promotion charge on track.
London started impressively, firing three points in the opening four minutes before top-scorer Pádraig McGoldrick and Mark Gottsche were both denied goals.
However, Paul Coggins’ side then went scoreless for 25 minutes as Wicklow grabbed a stranglehold around midfield and a late Seanie Furlong free gave Wicklow a 0-6 to 0-5 interval lead.
London were unlucky not to be awarded a penalty when Mulvey’s goal-bound shot was foot-blocked.
Instead, a late spot kick was awarded at the other end after Sean McVeigh impeded Furlong. Glynn sent Evan Byrne the wrong way to put an undeserved gloss on the scoreboard.
Scorers for Wicklow: S Furlong 0-6 (2fs), L Glynn 1-2 (1-0pen), T Hannon 0-4fs, R Finn 0-2, M McLoughlin, J McGrath 0-1 each.
Scorers for London: P McGoldrick 0-5 (1f), M Gottsche (1 45), E O’Neill (2fs) 0-2 each, L Colfer, S Doolan, M Mullins (f) 0-1 each.
WICKLOW: J Flynn; C Hyland, A McLoughlin, A Byrne; D Healy, M McLoughlin, S Kelly; J Stafford, R Finn; D Hayden, D O’Sullivan, L Glynn; T Hannon, S Furlong, J McGrath.
Subs: A O’Malley for O’Sullivan (51), N Gaffney for A McLoughlin (67), C McGraynor for Furlong (70).
LONDON: E Byrne; N Burke, S McVeigh, D McGreevy; K O’Leary, S Mulligan, A Gaughan; A Raftery, L Mulvey; P Sherry, S Doolan, M Mullins; P McGoldrick, M Gottsche, L Colfer.
Subs: E O’Neill for Colfer (49), G Crowley for Burke (51), E Mageean for Mullins (52), S Kelly for Gaughan (63), C McCallion for McGoldrick (70).
Referee: E O’Grady (Leitrim).