Jails in England and Wales are at "bursting point", prison governors have said as figures show there are currently only 160 spaces available.
Police station cells could be used to control the problem
Inmates are being moved around to find cells, said Charles Bushell, head of the Prison Governors Association.
Home Secretary John Reid has been discussing options such as deporting some of the 10,000 foreign prisoners.
The Home Office said capacity is set to rise to 80,400 by the end of the year, with a further 8,000 places planned.
But Mr Bushell said jail conditions could not be "squeezed" any further to try to create more places, and the situation was "desperately bad".
"The problem is that as you get fuller and fuller, more and more of your prisoners have to be whisked around the country," he said.
"And the problems that we have got in England and Wales are that we have now reached bursting point.
"I have to say that those are replicated, as far as I'm aware, in Scotland and in Northern Ireland."
Over the past 24 hours, the prison population has increased to more than 79,800, with room left for only 160 more inmates.
Mr Reid has been meeting members of the National Offender Management Service and Immigration and Nationality Directorate to discuss moves such as the early release of prisoners and the use of about 500 police cells, known as Operation Safeguard.
But Prisons Minister Gerry Sutcliffe told the BBC that Mr Reid was against early release.
Prison Reform Trust director Juliet Lyon called for decisive action from the home secretary.
"Faced with a crisis largely caused by successive home secretaries talking tough but failing to come to grips with effective prison policy, John Reid must now act decisively to divert petty offenders into enforced community work, addicts into treatment and the mentally ill into healthcare," she said.
Children's Society policy director Kathy Evans described prison population figures as "shocking" following a 6% rise in 15 to 17-year-olds locked up over the last year.
The Home Office said "all options" were open in trying to reach its target limit of 72,669 prisoners.
A spokesman said there were plans to build new prisons and expand existing ones through next year.
Conservative MP Ann Widdecombe was prisons minister from 1995 to 1997 when there was a similar surge in inmate numbers.
"I brought in a whole series of temporary measures - a prison ship from the United States, I brought [portable buildings] from Norwegian oil rigs and put them down in the lower security prisons.
"At one point we were poised - we didn't actually do it, but we were poised - to take over a holiday camp because.... all the accommodation is there.
"All you've got to do is close down the central facilities, and move a secure perimeter around the camp."
Liberal Democrat home affairs spokesman Nick Clegg accused ministers of "inexcusable incompetence".