Location: Propping up bars in the Lands of D H Lawrence and Bishop Bonner
I did a full-time PPL(H) in the UK and when I was making my enquiries, pretty much every school I contacted was happy to organise it. However, bear in mind that even instructors want some me time so it will likely be five days a week.
I would also recommend starting studying now. The exams aren't difficult but there's a lot of volume even at PPL. Best to start with Air Law, Met and Human Factors.
I was asked several times about this by prospective "intensive" students, and we agreed to do it as long as they kept up with the ground school, which basically meant doing at least 1 exam a week, if they were finish in 6 weeks.
my own limted experience was that in all cases apart from 1 the student let themselves down by not studying in the evenings enough to keep to the schedule, so we had to suspend flying till they caught up, they would use such excuses as "I'm tired from all the flying"
so before you start on your "intensive course" I would say are you sure you mean it? because its quite intensive
also I agree with the 2 trips a day and 5 days a week comments, more than that can be diminishing returns. also definitely start studying now and go in to do the exams even if you havent started yet, as long as you are ready.
I think the reason why most PPL(H)s are done over a period is down to he student, NOT the school. As Vee Any says, if you like Northumbria and the feel of the place ask them. I am sure they will try to accommodate you.
The previous advice cautioning about the student keeping-up is wise, in my view. You must have the relevant ground school done before it is needed for the flying. In general, the student will find full-time MUCH harder than the instructor. 5 days per week would be the max sensible, I suggest.