Well, I started flying on 25 March and went solo on 29 March. Q X-C on 12 April and PPL Test on 19 April.
That was back in 1968 when it was a 35 hour course. But I did it Cranfield, so it ought to be possible to do the whole thing in 5 weeks in the UK these days.
Admittedly we did fly 6 days a week - and I did my Q X-C on Good Friday!
I note that my PPL Test was on 19 April - yet the Board of Trade issued my PPL a mere 4 days later.....