Stuart Pearce's Team GB finished top of Group A after Daniel Sturridge's lone goal secured a 1-0 victory over Uruguay in Cardiff.
Should they come through a last-eight meeting with South Korea in Cardiff on Saturday evening, they will face hot favorites Brazil at Old Trafford next Tuesday.
Had Gaston Ramirez's injury-time effort not rattled the bar, they would have avoided that fate.
It is a shame too, because with Spain already out and Uruguay making their exit here in typically bad-tempered fashion, GB would otherwise be a strong contender to reach the final at Wembley on August 11.
Not that Pearce and his team should be criticised for that.
Sturridge's goal was the least they deserved from yet another encouraging display, which maintained improvement from previous matches.
At times, Britain's approach work was marvellous, with Aaron Ramsey flashing a first-half shot across goal, one of those that bisected the far post and the outstretched legs of Sturridge and Scott Sinclair.
The clock was ticking down towards the interval though when Allen wove a neat pattern inside the Uruguay box before drilling the low cross which Sturridge prodded home from close range.
The South Americans, so fancied beforehand, had been a major disappointment and this was no exception.
Luis Suarez was one of the major culprits too, who was often foiled by the imposing figure of Jack Butland, the teenage goalkeeper who is having such an outstanding tournament.
The 19-year-old denied Suarez in the second half with a full-length fingertip save, Edinson Cavani helping him out by belting the rebound into the sidenetting.
When he was subsequently booked for handball, the cheers at least made a change.
The next time he heard them was to signal the end of Uruguay's interest in the competition.