Stuart Pearce's side take on Uruguay in Cardiff on Wednesday night needing to avoid defeat to secure a quarter-final berth.
That would give further strength to a belief that GB should continue, providing a way can be found to navigate a complicated qualification criteria.
But Bellamy knows there are significant political obstacles to overcome.
And he does not believe they will.
"I am sure it would be beneficial and I would love to see it happen again," he said.
"From my own experience, it has been outstanding, one of the best experiences I have had as a footballer.
"But I this is probably the last time it will happen, which would be a shame."
Wednesday night's game will be GB's third in six days, putting additional strain on veteran duo Ryan Giggs and Bellamy, who has already contributed one goal and two assists to the GB cause.
With Spain bowing out and Uruguay likely to be condemned as well if Pearce's men complete their own task at the Millennium Stadium, hopes will start to rise of a rare major tournament last four appearance.
A fully fit Daniel Sturridge would be a big advantage for GB against a Uruguay outfit for whom star duo Luis Suarez and Edinson Cavani have so far failed to fire as anticipated.
Yet Sturridge is acutely aware how close he came to not being involved at all after a pre-tournament meningitis scare, from which the Chelsea striker admits he is yet to fully recover.
"I am getting there but I am still not 100%," he said.
"Basically I am a week behind the rest of the lads in terms of fitness because they had a week of pre-season when I was at my club.
"Also I have lost a bit of weight but I am getting fitter.
"This was the centre-piece of my summer and I was more than a bit concerned about missing it.
"It was the right stage to show what I am capable of.
"A week after contracting meningitis, I was unsure whether I would be coming or not.
"At that stage I certainly felt worse than I thought I would.
"Thankfully, as time went on I improved, although there were only a couple of days to go before we made the decision to go for it."
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