Hi Craig
Well... in theory yes, it's not too far to walk. If you were walking along a nice country lane, it would probably be quite pleasant... but this is London (and, he says, inviting protests, not the prettiest bit of it), with the crowds, the endless waits to cross roads, the ease with which you can get lost etc. so I'd say wouldn't rule it out, but you might get a bit fed up by the time you got there ! It's very simple to walk though from Old Street underground and the right exit is clearly signed (there are a lot of exits at that station so make sure you pick the right one to use). Think it's only a couple of stops down on the Northern Line.
Hope you get a better eye care experience than you've had up to now. My last bit of advice is that if possible, try to keep a clear idea in mind of what you want to investigate -- might be you'd like to try a different sort of lens if you're not getting what you want out of RGPs, say. In that case, make it known that you don't want another set of cheap 'n cheerful RGPs but maybe want to have a trial of Kerasoft lenses. I'm often tempted to think that the professionals are psychic and will just know what's bothering me and think up exactly what I'd like to do about it, but that's probably not a fair expectation so I shouldn't be disappointed when it doesn't happen
But what isn't unreasonable is if I spell out what isn't working for me, that is responded to and options are presented to me with a chance to go through the pro's and con's of each.
Do let us know how you get on, if you're unsure of anything (e.g. want any more information on a particular option you're thinking about) do ask but it does seem like you've been through everything -- and more ! -- in the past few years

.
Best wishes, take care, be hoping that all goes okay for you.
Chris