Squawk 2650 (and others)
The Heathrow Flight Briefing Unit numbers have changed recently. I'm sure you would have picked it up from the Notams.
Tel: 0208 750 2615/6
Fax: 0208 750 2617/8
Personally, I always try to telephone LHR to check that they have received my flight plan. I also double check that my departure aerodrome have it.
If I am doing a day trip to France for example, then I fax LHR and do the return leg with the French Internet service OLIVIA
http://www.sia.aviation-civile.gouv....et_uk.asp?m=14
which is excellent. Usually, OPS/ATC at home have both inbound and outbound flight plans before we set off for lunch.
The nice man from NATS told me at Booker last weekend that we should be able to file UK FPLs on the web by the end of the year.