I was doing the same a couple of weekends ago routing from the west overhead Stapleford and on to Earls Colne, with Farnborough Radar. On the way there, Farnborough radar asked for my intentions as I was approaching the Stapleford ATZ. I replied I intended to go through the overhead at 2200+ feet. They seemed happy with that and I remained with them.
On the way back as I was approaching the ATZ, I was asked whether I would like to change to Stapleford A/G for a few minutes, but retain squawk. So I said yes and did it that way.
I am a new PPL so on my return to base asked one of my instructors what was the most professional and/or safe way to do it. His view was negotiate a transit of the ATZ (which I take to mean do not necessarily squeeze above it and below London) or if not possible then go to the south of the ATZ. On reflection, I am inclined to think going to the south makes it more likely you will meet conflicting traffic arriving and departing from Stapleford, so my inclination is overhead is better.