By Tim Baker, political reporter
Just 100 male prison places are left, Sky News understands.
The Labour government has repeatedly accused the Conservatives of neglecting the justice system, leaving prisons at risk of overflowing.
Last month, Sir Keir Starmer green-lit plans for some prisoners to be released after serving 40% of their sentence - rather than the usual 50%.
But arrests in the wake of the recent riots as well as bank holiday events like the Notting Hill carnival, music festivals and football matches have pushed capacity even closer to a maximum.
PM: I can't build a prison by Saturday
Speaking in Downing Street this morning, the prime minister said: "I can't tell you how shocked I was when I discovered the full extent of what [the Conservatives have] done with our prisons.
"And it's going to take time to fix it. I can't build a prison by Saturday.
"We will fix it, we've already taken the measures that are necessary to make sure we can get through the disorder.
"But I shouldn't be sitting in the COBRA room with a list of prison places across the country on a day by day basis, trying to work out how we deal with disorder.
"But that's the position I was put in, and it's frankly not good enough."