England have been knocked out of the World Cup by a spirited Bangladesh who grabbed a quarter-final spot following their narrow 15-run victory in a tight Pool A match in Adelaide on Monday.

Put into bat, Mahmudullah struck Bangladesh's first World Cup century and starred in two key partnerships to lift Bangladesh to 275/7.

Three-times finalists England made a mess of their chase on an Adelaide Oval track that held no demons and folded for 260 in the penultimate over.

Bangladesh looked a bundle of nerves towards the end but Rubel Hossain (4-53) claimed two wickets in the 49th over to trigger wild celebrations.

England made a decent start to their chase before losing their way in the crunch match.

Adjudged leg before wicket on 11, opener Moeen Ali successfully got the decision overturned but the bearded right-hander was run out after a mix-up with Ian Bell (63).

England's problems were compounded as James Taylor perished chasing a wide delivery and Joe Root fell for 29.

Bell, who hit Mashrafe Mortaza for three boundaries in an over, pulled and drive with impunity, adding 54 runs with Alex Hales (27).

Mortaza dismissed Hales but it was Hossain's double strike in the 27th over that turned the match on its head. Done in by extra bounce, Bell was caught behind while Eoin Morgan hooked to the fine leg fielder to fall for his fifth duck in last 11 innings.

England's problems were compounded as James Taylor perished chasing a wide delivery and Joe Root fell for 29.

But Josh Buttler (65) and Chris Woakes (42 not out) injected life into the chase with some lusty hitting before Hossain dismissed Stuart Broad and James Anderson in the 49th over.