Regarding helicopters at LHR.....
Every so often we have police helicopters flying along the northern and southern perimeters. Yes, they appear close, but we only do this under certain cloud and visibility limits. We pass traffic information to every a/c, telling them where the helicopter is, and at all times we make sure the controller has the helicopter in sight.
Other helicopters crossing the airfield follow a procedure laid down in the AIP. Again, this is a 'good weather' procedure. The helicopter will be talking to the person controlling the landing runway, and he/she will identify a gap where it will be safest to cross the helicopter. He'll tell the helicopter to report when he is visual with the a/c that he is planning to cross behind, that done, the ATCO will warn the next landing a/c that a helicopter is crossing in front of him.
If the weather is not good, and the helicopter HAS to cross the airfield, rather than route around, then we need a big gap in the landing traffic.
PPL(H)s can cross Heathrow. However, I would advise that they know the AIP procedure inside and out. We find a great diversity of apparent ability in following the procedure, and it has been known for ATCOs to turn helicopters away if they have any doubts as to the pilot's ability to get it right. I would recommend any PPL(H), or anyone, who hasn't done the crossing procedure before to tell ATC, so then maybe we'll go for a bigger gap!
