I travel from a similar area. It’s hard work without a car to be honest - you might want to zipcar it, I’ve done that a few times.
Most has already been said but my experiences were:
Wycombe Air Park / Booker
I trained there ages ago when it was branded British Airways. It was my only point of reference at the time and I quite liked it. It had ‘proper’ (unnecessary I now think) ATC and was fairly well run although I had various instructors and they all taught differently which wasn't ideal. Tarmac runway wasn’t an issue ( if the wind was the right direction), but to be honest loads of lessons were weathered off and would have been the same on tarmac or grass.
I called a few times this year to discuss retraining after a lapse and found them to be curt, borderline rude, and completely uninterested. Whoever answered the phone sounded like a bored, 20yr old wannabe airline pilot (I came to that conclusion purely on the way they spoke to me) and they never answered a single email. So I totally ruled them out. Maybe I was unlucky - I was keen to go back there as it was where I first flew but I’d probably never bother again. They do have a big fleet seemingly PA28 and Cessna now.
A great airfield. I had a share there and did my IMC training and some aeros there. It could use a bit of love updating the decor, menus etc (literally hadn’t changed a bit in the years I was away!) but it offers a great ‘club’ sort of feel with nice place to hangout. Again it’s not the place I’d probably go if I wasn’t flying but it’s a nice social scene around flying.
I don’t think the grass is an issue and although I like the AG radio now I’m used to it - the first time I went there I didn’t know what to do not having to get permission to do anything!
They have more aircraft than instructors and I found it tricky getting anything booked in recently, after a bit of a mess up their end initially, and this meant quite protracted training even despite the amazing weather. Definitely check on availability if you go there.
I believe they are OK for their AC to be taken for the day post-PPL but i haven’t put that into practice yet. I think multiple days requires more heavy usage. Same everywhere really and a key reason (among others) why so many people without a share give up after getting their license .
Has tarmac and FISO and is close, so ticks a few boxes. I’ve only done a few hours there having discovered it only recently. It’s a good airfield, and has some more ‘bizjet’ (Jetprop) flying. Not much social scene but has a cafe. Training there is primarily Synergy and LTFC. Synergy is pretty expensive and you have to add instructor time on top of their rates, billed at ‘student contact time’ so may be a lot longer than your flight hours. An instructor was very over-enthusiastically teaching use of a whizz wheel while I was waiting there - ‘this is how you’ll plan your flights once you have your license’ he told his student. It made me laugh, what a waste of time I thought....
Didn’t visit LTFC but I understand they are more affordable and have their own ‘clubhouse’.
Both operations have their aircraft parked on the grass.
Of the two I flew with recently, Synergy at Fairoaks was most expensive and the aircraft felt a bit ‘rough around the edges’.
Waltham is slightly cheaper and the hourly training rate is what you pay, and the PA28’s I think are pretty well specced most with Garmin 430 and some look quite decent. You do have to pay membership but I think students get a discount.
Some people don’t care so much about the condition of fleet - especially in training - but I think for £200+ an hour you should be getting a nice aircraft. This is also important if you’re thinking of hiring afterwards, and will save the look of dread on your friends/passengers faces when they turn up to see an aircraft looking like it’s long past it’s sell by date and dirty/worn/smelly interior which you can still be paying £200/hr for around London.
I’d personally avoid anywhere that charges per landing or touch and go for training - it can really add up. I did some flying /checkouts from Shoreham when I lived near there and the airfield costs made it so much more expensive.
Just realised Blackbushe isn’t on your list - not sure how accessible by train but it’s similar distance to Waltham/Booker.
Good luck with it. Whatever you do once you’ve passed, try and keep flying....