I did my PPL and IMC rating at Booker in the late 1970s.
They had the PA-28 G-ATUB, TUC, TUD.
And the PA-38 G-DYOU, TOO, CAN, FLY.
And the PA-28 Arrow G-BAWA.
My flight instructors were Gordon ex WWII Hurricane pilot, and Joan Hughes mbe one of the most remarkable women in aviation history.
I've had a very successful career.
Now I'm looking into doing a (f)ATPL for my daughter.
I've looked into BCFT at Bournemouth and FTA at Shoreham and SFC at Stapleford.
I was planning on looking at Booker and am considering Diamond as well.
There are three important factors. Housing, instrument approaches, and landing fees.
For you, since you live 20 minutes away. I'd go with Booker.
My parents live in Surrey which isn't of much help. So for us SFC makes better sense. Housing on airport, many local instrument approaches, no landing fees, and a MCC/JOC.
Don't worry about where you got your license from. The old school tie is only good for hanging yourself with. Get your ticket to a wonderful career and get some experience.