As VeeAny says, there are specified helicopter routes. Helicopters are under ATC control long before they get anywhere near the airport.
The helicopter wouldn't be "doodling around" - it would be under strict control by LHR Tower in order to fit in with arriving and departing airliner traffic.
We're usually required to hold at the airfield boundary before being allowed to cross the active runways. Some people hover, some orbit. If you orbit it has to be tight, and very close to the boundary, to be ready to cross quickly the moment clearance is given.
We may also be asked to hold again between the runways, before crossing the next active. I imagine the pros prefer being cleared to cross in one go - I'm disappointed if I'm not told to hold over the middle of the airport, but I may grow up one day!
I obviously don't fly across LHR as often as many professional pilots but I've always found as a PPL that, despite being extremely busy, the Heathrow Tower and Thames Radar controllers are helpful and friendly - provided you comply strictly with instructions and read back (sometimes quite long) clearances correctly without the need for repetition. I've heard they can become rather less friendly if you don't! That's understandable and fair enough given their very high workload/volume of traffic.
The Heathrow crossing procedure works well and safely, and thankfully wasn't taken away in the knee-jerk reactions after 9/11 - long may it continue!
Tudor