Well, after a little web searching, I've found the definitive answer to EGLL (aka LHR).
May I draw the learned gentleman's attention to paragraph 1.b on page 2-EGLL-1-11 (I kid you not) from the Heathrow AIP, which you can download as a pdf from:
http://www.ais.org.uk/uk_aip/pdf/ad/EGLL.htm
(right click on the "textual data" at the top of the page, then save and browse the pdf - this will be quicker than left clicking it, honest!)
If you can't be bothered, here is part of said paragraph:
Light single and twin engined private aircraft will not be permitted to use the airport.
OK - no mention of ultra-fast PA28 requirements, but I did read somewhere that it was landing and take-off speeds which are driving this rule (to make traffic separation easier). Look at it optimistically - you've saved a sh!t load of landing fees by not being allowed
You
can however enter the London Control Zone under SVFR in order to transit and/or use another airfield within the zone (this is in para 13.c on page 2-EGLL-1-24)
There you go - no charge
[ 19 October 2001: Message edited by: sanjosebaz ]