Wayne Rooney returned with a goal but a controversial decison against Urkaine was harsh on an enterprising host side.
Victory over Roy Hodgson's side in Donetsk would have given Ukraine passage to the knock-out phases but a 62nd minute decision not to award the hosts a goal, despite the ball crossing the line, was enough to hand the three points to England.
Oleg Blokhin's team had to do without their talismanic captain Andriy Shevchenko for the first 70 minutes. The Dynamo Kiev striker was carrying a knee injury and only made the bench.
The first half was far from a classic but saw some moments of encouragement for the hosts. Andriy Yarmolenko was in exciting form, cutting in from the right and indulging on a jinking run which resulted in a corner.
Ukraine had barely composed themselves for the second half though, when Rooney struck. A Steven Gerrard cross took a deflection and bounced out of the reach of Andriy Pyatov in goal.
Rooney had the simplest of jobs to nod it over the line from one yard.
Soon after, the controversial 'goal' had Blokhin and his team seething. Marko Devic advanced on goal and beat John Terry with a turn.
His shot struck Joe Hart and looped into the air but Terry recovered to hook it away under the bar. Replays showed that the ball had crossed the line, and England had been let off.
The introduction of Shevchenko kept the momentum with Ukraine but they could not trouble the England back-line to the same extent again.
France's defeat to Sweden in Kiev mean England top the group, and go on to face Italy in the quarter finals.
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