I'm also not a great fan of integrated.
Whichever way you go, do two things first.
(1) A class 1 medical
(2) a UK or EASA PPL.
With those behind you, you know if you can meet the medical standards, and have the aptitude and dedication to push through pilot training. The £15k for the PPL or so may be the start of your modular route, the cheapest bit of de-risking you ever spend, or a lesson that this wasn't for you, or a an entry into an amazing hobby whilst realising that you'd rather earn your living elsewhere. All of those are good outcomes.
Committing to the £90k+ of an integrated course without at-least doing the PPL and all that will teach you is not, in my opinion, a sane act.
Close to Heathrow you have three really good PPL schools. Pilot Training Centre at Denham, Booker Aviation at Wycombe Air Park, and West London Aero Club at White Waltham. I've flown with all of them and whilst I have personal opinions and preferences, I doubt very much you'd regret any of them for this critical first stage.
G