I did it the reverse way with a mate (in the way-back, when I was in my 20s).
Spread it out over 2 weeks - sorry can't remember the exact route now, but definitely best to Start in Scotland and get the heavy hillclimbing over with in the first week, when you are freshest.
We worked it so we got a 2 night stop-over in Morecambe, on the middle weekend - and that 2 day break really did help - A LOT
I'll also add that when I was riding, I swore by my old Brookes leather saddle.
When a leather saddle is new - go out in the wet for an hour or so, with no rear mudguard - get the leather nice and wet, so it 'moulds' to your shape.
Unpleasant at the time, but worth it in the long run.
On a trip like this, a comfortable saddle is an absolute MUST HAVE.