Hi Dimensional:
I see you are a new PPL and your girlfriend has not flown in a light single before.
You are proposing to fly in a high-stress environment -- your first controlled airspace crossing and a particularly difficult one. I think most SEP pilots would not consider your Crystal Palace-Lea Valley route even if they knew every possible forced landing place like the back of their hand. Your workload will be high, navigating from field to field, and ATCO2's restrictions may compromise your ability to land clear.
For your girlfriend's first flight, why don't you chose a quiet route where you will have spare brain-power to explain to her what's going on, reassure her as neccessary, and make the flight a gentle, fun experience that she will want to repeat
Sorry if I sound a bit of a kill-joy, but I would really think again.