I would normally call in out of courtesy, but up there where it can be rather busy, I'd prefer to stay with the radar service. There have been some close encounters there on previous flights. And sure enough, tracking around it to the south I had two aircraft departing from Stapleford that climbed towards me in a turn. It would have been safer going over the top of the airfield.
Then it really comes down to your call as PIC.
It's perhaps unfair for Farnborough to have put pressure on a call you technically don't
have to make. My own view and I've routed over Stapleford often as I can't really see how to avoid it at times, is for the very short time one is talking to them the radar service is not as important as eyeballs on sticks. Not only have you got the flying training, you also have the LAM VOR and everyone who wants to squeeze between London City CTR and and Stansted CTA in the same airspace. The available headroom over the ATZ isn't a lot either so expect traffic from all directions at your level.
On the one hand I can see why you would want to stick to your radar service, on the other quite frankly in VFR you are much more into the realms of see and avoid, much like being in the vicinity of any busy club circuit without full ATC.
My point being, would you totally rely on a radar service in an area with flying training, people doing navigation turns in the same airspace etc etc. I wouldn't, there isn't time for them to warn you.