You have chosen a busy route for a new PPL, I did a similar route after a good number of hours post PPL and it was still a busy trip.
Watch out around Booker and White Waltham - they come at you from all directions! Even talking to both towers it was still very important to keep a very close eye out the window, whist also navigating carefully.
I also did a similar trip a few hours post PPl, me and a flying mate took our instructor and did the Burnham to Ascot SVFR route, this is a low level (not above 1000' agl!) under the western approach to Heathrow! Great fun, they will only allow one plane at a time in any direction so it may not always be available. Also, Heathrow wont let you through if you sound like you are not confident on the radio - we let the instructor do this bit of the radio!
Which ever route you do,, maybe worth taking an instructor with you for this bit of busy airspace?