I travelled down from Lancashire and think i saw Dr Edwards who diagnosed me following a very unpleasant local NHS rheumatoligist appointment which resulted in me being told (with a smirk) 'everybody your age has aches and pains'.
With the London hosp. I had plenty of time to feel I had been listened to and he was very pleasant and easy to talk to. He noticed the livedo reticularis all over my arms and legs, my rashes, my swollen hands, gave me an eye test for Sjogrens (the test sticks ended up glued to my eyes) which was positive, confirmed 2 of my 3 positive anti phospholipid tests were NOT normal (my local rhuemi said the results meant nothing), advised me to take aspirin for that, reassured me no end and confirmed it was 'highly likely I had SLE, but it is mild so please do not worry too much' and recommended my GP start me on plaquenil, and said he would be happy to see me again in the future - this advice he also gave my GP.
In short problems that had been going on and getting steadily worse for many years were dealt with in one 30/40 minute appointment, which effectively saw me given treatment that could reduce the consequences of my condition no end.
I went privately and it was worth every penny. I now have a local rheumi who not only actually believes SLE exists, but can also be serious, and is therefore worth early intervention.
Without my trip to London i would probably have ended up convinced i had a psychiatric condition, remained in pain, and ended up depressed whilst pushing myself to work full-time however i felt becasue it must all be in my mind!
Good luck. Just remember to write a little list and if you can get any relevant results from your gp to take with you do so to save time.