Despite running out convincing winners at Ruislip, Fergal O'Donnell believes his Roscommon side are still playing within themselves.
The Connacht champions dominated, but struggled to convert possession into scores.
"I'd have taken a 10-point win if you'd have offered it to me before the game, but after half-time we didn't push on," said O'Donnell. "We made a lot of mistakes."
Roscommon hit a late flurry of scores in the first half to lead 0-7 to 0-4 at the interval. London did narrow the gap to two after the restart, but Roscommon fired 1-2 in the final four minutes, with Senan O'Grady netting an injury-time goal.
Scorers -- Roscommon: S O'Grady 1-2, K Higgins 0-4, J Rogers (1f), G Heneghan 0-2 each, C Shine, C Cregg, D O'Gara, J Dunning 0-1 each. London: E O'Neill 0-3 (3f), J Collins 0-2, P McGoldrick, S Kelly 0-1 each.
Roscommon -- M Miley; S McDermott, D Ward, S Ormsby; N Carty, D Keenan, S Purcell; M Finneran, K Higgins; S O'Grady, D O'Gara, C Cregg; J Rogers, C Shine, G Heneghan. Subs: J McKeague for Purcell (4), J Dunning for Rogers (42), F Cregg for O'Gara (49), C Beirne for D Kennan (49), C Devanney for Shine (60).
London -- E Byrne; D Donnellan, S McVeigh, D McGreevy; N Tuohy, T Gaughan, A Savage; J Scanlon, C McCallion; C Conneely, J Collins, A Concannon; S Boyle, E O'Neill, L Gavaghan. Subs: D O'Neill for Gaughan (26), K Phair for Gavaghan (h-t), P McGoldrick for Scanlon (h-t), S Kelly for Savage (42), D McCusker for McCallion.
REF -- G McCormack (Dublin).