I believe in California more than two hundred male prisoners are currently applying to be transferred to female prisons.
Several incentives for even men not identifying as trans, especially if their sentences are long:
Less likely to meet violence from people stronger than they are, more likely to have access to heterosexual sex and, for those who prey on women, more prey. Also, women's prisons tend to be somewhat more comfortable places on the whole, I've been told.
It seems that California doesn't require any medical transitioning or anything beyond a self-identification, so trying for this makes sense much more widely than just for those who actually are trans-identified.
That's not the UK, of course. But the data from the US, Canada, and the UK all suggest that a much higher percentage of trans women are in prison for sexual assault than is the case for male prisoners, on average. This, to me, would suggest that the scrutiny for that possibility should be central in deciding who can be moved into women's estate.