50 years ago tomorrow, I started my PPL course with the Bedfordshire Air Centre at Cranfield on the Cessna 150. The 35 hour course was very similar to the current LAPL(A) course, only the latter has rather better privileges for brand-new licence holders.
Like you, Dylan V, I had some previous cadet experience but it was 'A' and 'B' gliding badge level only, with a couple of passenger trips in light aircraft.
First PPL course flight: 25 Mar 68
First solo: 29 Mar 68
QX/C: 12 Apr 68 (Good Friday!)
PPL test: 19 Apr 68
Total time: 20:20 PU/T, 14:40 PIC
So it should be possible to complete a 30 hr LAPL course in 4/5 weeks, but only if you devote 6 days per week to it (as we did) and don't have any other commitments.
Once you have a LAPL, you can upgrade it to a PPL when funds / experience allow.
The problem will be to find a school which isn't stuck in the 'always done it this way' mold and actually knows about the LAPL!