One of the reasons I decided not to go down the private route was because of the time it would take to get to London. It wasn't so much the issue of how long it took to get somewhere in labour, but the whatifs, in case of there being something not quite right.
I choose a hospital which is about 40mins in good traffic, about an hour in peak traffic, and if there is an accident you are really screwed. I do feel this was as much as I was comfortable with and longer than a lot of women would consider.
I didn't have any problems but I did have a panic at 30weeks about reduced movements, and went to get checked. It was a LONG journey under those circumstances. It turned out to be nothing. But I do wonder what I'd have done if I'd chosen to go to London. Would I have got checked? I'm not entirely sure if I'm honest as I was reluctant enough to inconvenience DH to take me all that way and miss work. And what if there had been a problem and I'd decided not to go. Being at least reasonably close did offer reassurance and did mean I did get checked out.
This is why I do say, to really consider what going to London means. And to explore other options. You can choose which NHS hospital to go to, so you can still pick one closer but not one you've dealt with before. (This is effectively what I did). I really would try and resolve the issues you have rather than going to London if you can. Running away to London won't resolve a lot of those underlying anxieties.
I had a lot of extra support because I had a lack of trust in doctors and flagged it up as being something that was effecting me profoundly. Long term its been very beneficial and healing of old experiences.