there is already a mechanism for trans women, they could just use those facilities?
There are mechanisms - there literally isn't the physical infrastructure to cope with more than a tiny number.
One of the reasons behind prison riots is the abysmal physical condition of the prison buildings and their facilities: these are crowded beyond capacity (and the reality of this varies from one region to another with some having spare capacity and others being more overcrowded.
This week's Howard League count of prison numbers and overcrowding for England and Wales reports 82,846 prisoners in England and Wales (including Young Offenders):
Prisons are extremely overcrowded. Under the Ministry of Justice’s own definition of safety and decency, the prison estate should not hold more than 75,346 people. There are currently 7,500 men and women held above this level. Overcrowding is not evenly distributed across the prison estate, so some prisons hold many more people than they are designed to do so safely.
howardleague.org/prisons-information/prison-watch/