OP, you have lots of options nearby.
There's an up-coming Pilot Careers Live event at the Sofitel Hotel in Heathrow. The tickets are cheap and it's really worth going from experience. There'll be lots of schools and airlines selling themselves to you, and maybe you'll like the sounds of some of them. The important bit is that you don't pay too much attention to the big schools with fancy marketing - like L3, Leading Edge and FTE. Instead, talk to the smaller schools, like Stapleford and Aviation South West that have good reputations for modular training. Ask any questions about flight training, costs, the graduate prospects etc, and take every freebie that they have
. FYI, don't bother with the priority tickets as you'll spend much more time in the main hall talking to all the schools than you'd think, so you'll miss the theatre talks on your first time going.
Having said that, modular is the safest option; even if thats a full-time modular course. The ideal path has been discussed here countless times by rudestuff and co., and is also suggested by Bristol Ground School.
https://cdn.wingsalliance.eu/wp-cont...Costs-2023.pdf I've done a sum of flight training, landing fees, tests, equipment etc at ATOs in/near London and £60000 should be a safe number, excluding any travel and living expenses obviously. Near Heathrow, your local schools are Blackbushe, Redhill, Flight Training London in Elstree, and possibly EFG at Biggin Hill. Stapleford is an obvious shout if you're willing to travel a little further. I'd get dual-license, limiting you to FTL and Stapleford for an EASA ATO.
If you're incistent on integrated, people tend to suggest ACS Perth. It's a 'fast-tracked' modular course, like Aeros, up in Scotland that provides dual-license. Aeros is another good shout but they've gotten significantly more expensive in the past few months. Bear in mind the expenses of living away from home for these two schools.
It seems like you have a good budget, and are looking for the fastest and most fun way of getting the fATPL, so the flashy integrated schools are looking appealing (rightly so). However, it's a lot of money to be playing chicken with, and ultimately you want to set yourself up for the best possible career prospects. What happens if an integrated school suddenly folds and you're left with nothing, or if the school has significant delays and you're supposed 18 month course is closer to 24+ months, or just a poor level of training? You've given them all your money already so you're hands are tied. With modular, you can bounce after you've completed your module and look for better elsewhere, hence forcing modular schools to maintain high standards.