You can be a Newson clinic patient online because they offer online appointments - that's how I see them. I see Dr Jane Robertson there and would really recommend her. Your meds will arrive in the post a couple of days later, via CloudRX pharmacy.
They will accept any bloods that have been done including by your GP (as long as they are within the last 6 months I think). You can use NHS bloods or Medichecks.com bloods (as long as you get the venous test) and I will report back on this, but I think they are going to accept the Randox Tasso device (which takes a home blood draw from your arm, where you usually get injections). The only tests they won't work with, are finger prick tests - because they are not reliable.
They will write a letter to your GP afterwards and tell the GP what they have prescribed and ask the GP to continue that prescription on the NHS - so you don't have to pay for meds. The GP is not obliged to follow that advice, but I'd think if you have a helpful and cooperative GP, they hopefully will. Then you will get the meds for free. That's what I do, and my GP provides it all even though my estrogen is high dose. (I do think she is a bit suspicious about whether I need that dose but she has cooperated so far!)
Then you need an annual appointment with Newson to stay registered with them - and they will update your GP each year. Give them a call and ask any questions you have, they are v helpful. The annual appointment is £240 (I think).
In terms of - if you try something and you don't like it etc... Newson will often be more flexible in terms of what they prescribe, to allow you to experiment more than your GP would. For eg when I first started, they told me to begin on 25 patches for a few weeks, then increase to 50, for a few weeks and if I still had symptoms to increase to 75. So they equip you with more than just one dose.
But if you do need to completely change product then you have to have a 10 min phone consult to get that approved which is £100. I had to do that with Sandrena - I asked to switch to that because I was on 12 pumps of Oestrogel(!) and not absorbing more than 6 pumps (levels had not gone up). I switched to Sandrena at my annual review but then I couldnt' absorb the Sandrena at all and it was awful, I had a return of everything really quickly. So I had to pay for another phone consult and they put me onto a combo of gel and Estradot patches which is now working well. But basically you will get what you want, fast.
I think it is worth paying to find out what works for you, and hopefully with your NHS GP then continuing it with free meds on the NHS. I also like having a fallback should the NHS be out of stock of something. They have been out of stock of Oestrogel, utrogestan and now Estradot patches - and every time, Newson and CloudRX have come through for me and I've been able to get what I need that way. It shouldn't be like this, but it is...