I have just gone private for treatment on roaccutane as the waiting list for the NHS was so long. I could only afford to do this because I have medical insurance through work.
Each consultation is around £250 (paid for by insurance, mine only covers consultations), but on top of that, you have the cost of regular blood tests and prescriptions. Some GP's will do the bloods for you even if you are paying privately, however each prescription, depending on your dose, is anywhere between £50-£100 every month. My initial bloods, if I hadn't got lucky with my GP, would have cost around £400 (lipids, liver function, full blood count and pregnancy blood test).
I am absolutely not saying this to put you off going private, far from it, but I wish I had found some transparency around this when I was in your position, as everything I found online was very vague! It is very expensive and every private clinic/hospital will differ, so it might be worth investigating this before committing to a consultation.
I'd also do loads of research before you go on the types of treatments offered that might help you. Roaccutane was my only option left, as I had tried creams, contraceptive pills and two rounds of antibiotics. I did a lot of research on this medication beforehand too and knew it was what I wanted. There are a lot of scary things about roaccutane on the internet but I can honestly say I have had no problems whatsoever, 2 months in, other than extremely dry skin which I expected, and friends of mine who have been on it in the past have had the same experience.
Long story short, its very expensive to go private, there is no doubt about that, but once the initial consultation and bloods are out of the way, then its mostly just the prescription that will cost you, paid each month, so its a bit more manageable. Your derm will decide how often you require additional bloods and follow up appointments - mine are every 3 months.
If you decide you can afford to, I would absolutely recommend going private, however if not, get on the NHS waiting list as soon as you possibly can. In my area, it was around a 6-8 month wait - ask your GP if they have any idea how long it might be for you to help make your decision.
Please message me if you have any more questions, more than happy to answer
PS: I LOVE the username brianbadonde. Big Fonejacker/Facejacker fan here...!!