The majority of cadetships, albeit the Atlantic Airways one, don't require you to hold a single hour of Flying, let alone a PPL.
From what I've read, your ultimate aim is to get yourself a place on one of this schemes.
From past experience, and many others will tell you, holding a PPL may give you something to relate too during the interview stage, but it's not going to help you pass the aptitude, maths and physics examinations.
My advice would be hold that £7k back, apply for the airline tagged schemes, if your fortunate enough to make it through, great. If not, get your PPL and follow the Atlantic or the modular route!