The hosts beat Japan 71-55 in Group B to make sure of their place, with Terry Bywater scoring 19 points and Simon Munn adding 15.
Britain seized control early and pulled into a 60-32 lead before a late Japanese fightback.
Britain's win eliminated Japan and meant the pressure was off for Poland against Germany, a match the eastern Europeans lost 73-63.
Jan Haller led the Germans with 17 points while Sebastian Wolk added 15 and Andre Bienek 13.
Mateusz Filipski had 27 points for Poland with Piotr Luszynski adding 22 to combine for more than 75 per cent of Poland's scoring.
At the top of the standings, both Canada and Australia completed pool play with perfect 5-0 records.
Canada finished their Group B campaign with a 68-42 win over Colombia in which Dave Durepos had 18 points.
The outstanding Patrick Anderson took an extended breather, with all 13 of his points coming in the first quarter before he watched the rest of the game from the bench.
In Group A, defending champions Australia answered with a 68-48 win over Italy, with Brett Stibners scoring 17 points and Nick Taylor 14.
The Group A picture below Australia was only settled on points difference, with the USA's 63-55 win over Spain leaving both teams alongside Turkey with a 3-2 record.
Turkey took second place, ahead of the Americans and Spain.
Australia will now face Poland in Wednesday's quarter-finals, while Canada are paired with Spain.
The USA take on Germany and Great Britain face Turkey.
In the women's tournament, the quarter-final spots were already taken but the USA still provided some drama as they stormed back from 11 points down in the fourth quarter to beat China 68-65 in overtime and claim second place in Group B.
The win lifts the USA to second place in the group behind Germany, while China settle for third.
Germany finished top after completing pool play with a 68-28 defeat of Mexico.
Mareike Adermann led Germany with 18 points and Marina Mohnen added 16.
The Germans will now face Great Britain in tomorrow's quarter-finals after the hosts fell to 1-3 with a 67-50 loss to Canada in Group A.
Mariska Beijer was back to her best as the Netherlands beat Brazil 55-42 to take second place in Group A, behind Australia and ahead of Canada.
All three teams finished with a 3-1 record with the standings then based on points difference.
With Germany facing the Host Nation, tomorrow's other quarter-finals will see Australia tackle Mexico, Netherlands play China and a showdown between the USA and Canada.