There is a clinic in Brighton called wellBn (or maybe wellBN1). They are very trans positive and will take patients from all across the country to allow them or access gender affirming care. They currently have a wait list of 2 months or so to get seen, but that's not bad. Might be worth checking their website and shooting them an email.
I'm afraid I've no idea of costs, I presume just the NHS prescription charge so £9 per med. Yea their website is not great but if you email them a person will get back to you and they're super helpful and friendly. They've helped out a lot of trans people (and got a lot of stick from the Telegraph etc). I don't even think you'll need to travel, online appts and then pick up from your pharmacy. Best of luck!