Thanks for that PM

!
It looks like you can get an appointment there pretty quickly (within a week). It also looks as if they might be quite pricey (then again, you get what you pay for). One of the things I wasn't too keen on was the lack of explanations of pros and cons of the described procedures, but that doesn't always reflect the actual philosophy of a practice (the marketing people may have been at work here

- I'm sure you know all about it...).
But if you're interested in the place, I'd e-mail them, briefly explain the situation, and ask if you can get the dentist's private e-mail address. It's oftentimes easier to judge if someone might be suitable from their e-mail responses. Actually, I'd try and get both dentists' private e-mail addresses (if you can) and then compare responses.
I know it's a bit of an awkward situation with that other recommendation being part of the same "chain", but I'm wondering if it would be possible to get in contact with that dentist directly (e. g. by e-mailing them and asking for his private e-mail, by phoning and asking if he could give you a call when he's free, or by simply explaining the situation to the receptionist). I know you've had bad experiences with the receptionists at your current dentist, but the situation may be entirely different at the other practice. What I might do if I was in your situation would be to give them a call, explain to the receptionist that you're extremely anxious about dental visits after some bad experiences, and that someone mentioned that (insert name of recommended dentist here) might be able to help - and would it be possible to either meet him for a chat/e-mail him directly/talk to him on the phone (whichever you prefer). If the receptionist is sympathetic (and many are), you may even want to tell her that the situation is quite delicate because you are currently registered with an NHS dentist in the same group and he seems like a nice guy, but you feel you need someone who's especially good with nervous patients. That way, you could be open about what's going on, without offending anyone.
That might be one way of going about it.
I suppose my concern is that if I did manage to get an appointment at the recommended place, they would ask about my history - including where I'm currently registered.
Just leave that field empty? Or do they actually read out the questions to you?
Or alternatively, be straightforward about it - saying that someone seems like a nice person but you need someone who's very good with extremely nervous patients wouldn't really be offensive in any way.
The last thing I would want is for them to say "we saw one of your patients today" - if they turned out OK it wouldn't matter because plan A would go out the window, but if for some reason it didn't work out, then I would probably have some potentially awkward questions to answer.
I wouldn't be so sure that practices that are part of large chains actually communicate with each other on an informal level

. This might only really come into play if you *did* decide to switch, in which case they'd want your records sent over.
What do I actually need to say if I email one of these places? I know I'm after a second opinion and to find out what they're like, but I don't really want to lead them into believing I'm registering as a patient permanently in case they don't turn out to be OK, I don't really want to be in a situation where I've committed myself to signing up for anything unless I'm completely sure.
If you're only meeting someone for a chat, you don't have to make any decision or commitment until you're actually sure that you feel happy and comfortable with that person. You've got the letter - you could put something at the end of it along the lines of "I'm now looking for a dentist who can help me with this, and if you're prepared to do so, I'd like to have a chat with you" (<-- not that exact wording, but you get my drift).
If you pay in cash for the chat, I don't see any reasons why you would need to make a commitment of any sort. You can bring up your concern about being able (or not, as the case may be) to afford private treatment during the initial chat.