LGW used to offer overhead transits in the good ol days, but i haven't managed to get one in the last 5 years..
I'm not sure it's 'illegal' to fly over LCY in a single, just Rule 5(3)(c) to comply with, as i guess it's probably a congested area. Doesn't seem to prevent the annual airshow there though
Why not get your NPPL first and then worry about the difficult bits?