Ray Cox was put through by a Robbie Lowe pass for a 33rd minute goal that turned the tide in favour of Leitrim, who led by 1-4 to 0-4 at the break.
In the last 15 minutes Leitrim went 0-7 clear after Ray Cox shot over twice with James Glancy and Darren Sweeney adding a point each.
London replied with consolation scores from sub Eoin Mageean and David McGreevy.
Scorers for Leitrim: R Cox 1-3 (1f), J Glancy 0-4 (1f), R Lowe, P McGowan, D Sweeney (f) 0-1 each.
Scorers for London: E O’Neill 0-3, P McDermott, M. Mullins, L Mulvey, E Mageean, D McGreevy 0-1 each.
LEITRIM: C McCrann; A Wynne, C Egan, P Maguire; D Beck, C Sheridan, W McKeon; D Sweeney, P McGowan; P Brennan, R Lowe, G Hickey; A Croal, J Glancy, R Cox.
Subs: T Beirne for Croal (52), D Gilhooley for Glancy (61), C Ryan for Hickey (64).
LONDON: Evan Byrne; S Hannon, S McVeigh, D McGreevy; T Gaughan, S Mulligan, B Kerr; A Rafferty, L Mulvey; F McVey, P McDermott, S Doolan; M Mullins, E O’Neill, P Sherry.
Subs: C McCallion for McVey (41), S Bradshaw for Kerr (58), C Hands for Gaughan (60), S Kelly for Mullins (67), E Mageean for McDermott (61).