tc_atco
In defence of the guys who get it wrong, I think that there are some easily solved (free, by NATS) human factors issues here.
Firstly the ATIS says to give the information on "first contact with Heathrow" (no mention of "Director") whereas some of your TMA colleagues transfer aircraft to "Director" (no mention of "Heathrow").
Secondly, some approach charts have "London" in large font and "Heathrow" in a smaller style. Since AC and TC controllers are forever telling people to contact "London" rather than "London Control", I think it is very likely that some people check in with TC SE INS/BIG/LAM etc and give the information to them thinking (as they can clearly see from their map display that they are almost on top of the aerodrome) that they are talking to "London Approach" or somesuch. Of all the occasions that I have heard aircraft erroneously give their details to a TMA controller, I've only once heard that controller explain that they actually need to give all the information again when QSY'd.
On a related note to my first point, it may be that irregular vistors don't realise the connecton between reporting aircraft type and being provided with the correct vortex spacing. I would not be surprised if some people were expecting to report their aircraft type to the TWR controller for route charging reasons, for example. Speculation on my part, but I don't know why I need to tell some en-route controllers my registration (although I can have a pretty good guess).
So to fix some of the problem: someone needs to get their finger out and fix the ATIS to say "Heathrow Director", a gentle reminder could be sent to the TMA controllers that they need to tell crews who check in wrongly who the correct recipient should be and AC need to transfer aircraft to "London Control".
My 2 cents.
Incidentally, the only other place that I can think of that requires aircraft to check in Heathrow-style is Copenhagen. This is also one of the only other places we are regularly, intentionally vectored accurately to the minimum vortex spacing.
G W-H