A 67th minute penalty from Michael Meehan was the icing on the cake as Galway scored a comfortable 1-18 to 1-07 win over the Exiles at Ruislip.
Galway led by 0-06 to 0-01 after the first quarter, but scores from
Adrian Moyles, Kevin Downes and Kevin McMenamin saw London cut the gap to four points at half-time (0-08 to 0-04).
With Padraic Joyce pulling the strings, Galway built up an 11-point
lead before substitute Mark Alcorn found the visitors' net with a
speculative high ball in.
However, a push on Matthew Clancy allowed Meehan to fire home the clinching goal.
It was a positive performance from Liam Sammon's charges who pushed all the right buttons, but they never looked like hitting top form and will have to move up a gear or two as the Championship progresses.
Galway were in control in the opening 16 minutes and held command in the midfield area to ensure some effective possession for their attack.
Gareth Bradshaw, Nicky Joyce and Michael Meehan were all on target in the opening quarter as London failed to score until the 16th minute with a point from John Hughes.
It was the only score from the Down native in this game and while
London's scores were thin on the ground, a total of seven players got on the scoresheet for the hosts which was certainly a pleasing statistic for their manager Noel Dunning.
In a competitive second quarter the sides matched each other point for point until the interval.
Sean Armstrong was on target to push the Tribesmen back into a
five-point lead before Moyles thumped over his only score in reply.
Bradshaw added a score for the visitors before Donegal native Kevin McMenamin cancelled it out for a 0-7 to 0-3 scoreline in the 27th minute.
A Meehan pointed free restored Galway's five-point cushion but London were hot on their heels with Kevin Downes having the final say before the short whistle.
Galway, for whom Armstrong and Nickey Joyce missed some gilt-edged goal chances, were on fire on the restart and quickly latched over seven unanswered points in a nine-minute spell.
Meehan bagged a brace, Armstrong kicked three and half-time substitute Fiachra Breathnach and Cormac Bane were also on target.
London's first score of the half arrived from Pauric Duffy, but Galway had already cemented a strong lead.
Alcorn's goal, who saw Galway goalkeeper Adrian Faherty deceived by the bright sunshine, cut the gap to 0-17 to 1-06.
But the hosts could only manage a further point and Meehan's
successful penalty kick, after Clancy was fouled, sent them Tribesmen through to meet Sligo at the semi-final stage on Sunday, June 28.
London: M Alcorn 1-00, K Downes 0-02, J Hughes, A Moyles, K McMenamin, P Duffy, M Hughes 0-01 each
Galway: M Meehan 1-05, S Armstrong 0-05, G Bradshaw, P Joyce 0-02 each, N Joyce, F Breathnach, C Bane, D Dunleavy 0-01 each.