Just to clarify an earlier posting which listed a load of fax numbers....
If you need to fax a flight plan there are only 3 'parent ATSU' units and they are
Heathrow EGLLZPZX fax no 020 8 745 3491/2
Manchester EGCCZQZX fax no 0161 499 5504
Scottish EGPXYFYX fax no 01292 671048
Which one you need to use depends upon your intended departure point. There is a map in the Safety Sense leaflet which can be found at
http://www.srg.caa.co.uk/includes/ga/20aleafl.pdf