A Buckinghamshire prison only has 11 spaces left while others in the county are nearing capacity.
HMP Aylesbury currently has 391 inmates, the latest figures published by the Ministry of Justice (MoJ) show.
The institution – a category C training prison – has an operational capacity of 402, according to the data, accurate as of February 23.
Two other prisons in Buckinghamshire are also feeling the pressure.
HMP Woodhill in Milton Keynes and HMP Grendon Springhill are both 27 spaces below their capacity.
The MoJ told the Local Democracy Reporting Service: “Thousands of places are also being created through the expansion of prisons through additional house blocks and major refurbishments at existing prisons.”
It added: “This includes 194 places that have been added through refurbishments at HMP Aylesbury in Buckinghamshire.”
Justice Secretary Alex Chalk announced on Monday that prisons would be able to release ‘certain low-level offenders’ up to 35 days before their sentence was due to end.
In a written statement, he also said: “We are on track to deliver 10,000 new prison places by the end of 2025 and have a long-term commitment to build 20,000 new prison places overall, the largest prison building programme since the Victorian era.”