Hi, and welcome!

There are quite a few late transitioners here at Susan's, and some of us are also based in the UK.
I'm afraid there aren't many gender therapists in the UK; most work within the NHS and most of us have to travel quite some distance to see them. For example, I live in the rather large city of Bristol, but in order to see a private gender therapist I would have to go to London or Cardiff, or for an NHS GIC my closest ones are in London or Exeter.
If you want to go private, there are two reputable clinics in London that you could go to. One is called GenderCare, and is run by Dr Stuart Lorimer who also works on the NHS at Charing Cross. The other is called Transhealth, and is run by Dr Richard Curtis, who is himself a trans man. Both of these clinics can give you the therapy you require, and both of them can prescribe hormones if you wish. Their appointments range from £150-£250 per session, and there is a wait to see them as their services are in high demand.
There's also a delightful trans woman psychotherapist in Cardiff named Alex Drummond. She is highly reputable and will certainly give you the counselling you desire, but I don't think she's able to prescribe hormones or anything.
If you want to go the NHS route (which is recommended, as it's, y'know, pretty much free) then there are seven clinics in England that you can go to, and you can choose whichever one you want irrespective of where in England you live. They all have different waiting times for the first appointment, and some of them are ridiculous. Current approximate waiting times for a first appointment are: Charing Cross, London (13 months); Leeds (4 years!); Newcastle (4 years!); Daventry (4 months); Nottingham (12 months); Sheffield (18 months); The Laurels, Exeter (8 months). So the quickest one is Daventry in Northamptonshire, but as you're in Dorset you might find that your best bet would be to ask for a referral to The Laurels in Exeter.
Your first step for the NHS route is to go to your GP and ask them to refer you directly to the clinic of your choice. They'll send the referral to the clinic, who will then write to your local health authority to ask for funding for you. Once that's received, they'll send you your first appointment.
If you want to go private, simply ring the clinic of your choice, but please be aware that all services are oversubscribed at the moment so you might have a wait of several months.
Good luck!