Starting at the end, it's legal to sell sex in the UK. What you can't do is advertise the fact that you are available for cash in person, on the street or other public space. So avoid street work, and you are fine.
Sex work can be good for people with mental health issues because you can often pick hours etc to suit your needs. It can also be horrible if something triggers flashbacks or other symptoms.
Sometimes there are choices you have to think about. So brothel work can be safer - there are always other people around - but it means having those hours set by others and the brothel options for trans people are many fewer.
Yes, there is transphobia, especially towards post-op trans women. As - from the sound of it - a trans man, there is much less of it, but also a smaller niche in the market.