Unfortunately level busts happen throughout the country every week , we get a list of them through the weekly reports , aircraft have to be broken off and repositioned , which at a small unit causes no end of problems but at units such as Heathrow Gatwick etc can cause considerable difficulities.
If you are displaying mode C you should, if wearing an allocated code have been verified, thus we will know if C is working within parameters. If the altitude displayed is within 200ft of that stated it is verified thus you could have in theory just 600ft between aircraft using a 1000ft seperation.
Climb say an extra 500ft , see what im saying.!!!
I believe remembering from my EGLL days that in the area you are talking about that aircraft into EGLL drop not below 4000ft , that could well have changed, so the likelyhood of you hitting something climbing to 3000ft would be low however at certain times (and I said this is going back a few years ) Thames would tell EGLL that they could have 3000ft if they had no traffic to affect.