Ibz Diallo scored the hosts’ solitary reply as goals from Anatolii Shevchyk, Oleksandr Devlysh (both two), Volodymyr Antoniuk and Denys Ponomaryov made it six points from two games in Pool B for Sergiy Ovcharenko’s side.
Shevchyk said: 'The match was quite tough, it certainly wasn't easy. Great Britain were strong, and showed a lot of fighting spirit. They were trying hard until the very last moment.
'The game was well-paced, and Great Britain were a decent and honourable opponent.'
Britain’s conquerors in the first round of games, Brazil, will also feature in the final four after putting eight goals past the USA.
Four players bagged braces as James Hoffman Jr’s charges failed to break through the Brazil defence.
Also progressing to the knock-out stages were Beijing silver medallists Russia, who repeated the scoreline from their opening game against Argentina with an 8-0 defeat of the Netherlands in Pool A.
Viacheslav Larionov got the Russians off the mark before completing his brace in the second half. Eduard Ramonov and Lasha Murvanadze also scored twice with George Van Altena putting through his own goal.
And completing the final four will be Iran, who put on a much-improved performance following a nervous opening victory over the Netherlands to see off Argentina 8-1.
The USA will battle Great Britain to avoid finishing fourth in Pool B, with Brazil challenging Ukraine for top spot.
British men’s coach Lyndon Lynch was optimistic, saying: 'The USA are ranked more in the bottom half of the world.
'We have beaten them three times already this year so, yes, I am looking forward to lifting the boys up for that match.'
Iran face a tricky test to end up on top of Pool A as Russia continue to score for fun at London 2012.