Will let you know if I find something out.
Apparently there is some sort of "hotel hoppa" bus service from LHR terminals to hotels in the airport area, I'll investigate this a bit more and let you know.
See ya there!
Added about 2041UTC:
Ok, this what I found on the BAA website.
There should be a Hotel Hoppa service (726) from LHR terminals 1,2,3 bus station (central bus station) going to the Renaissance LHR, the service also runs to and from Hatton Cross tube station which is good for me

Frequencies are about every 14mins from 05:30 to 23:30 hours approximately
Map of routes here:
http://www.baa.com/pdf/travel_around_hal.pdf
Tickets seem to cost £3.00 each way..

if on a *very* tight budget (e.g. meself) , but if there's no other way might just as well
I think this helps

, well then definitely see y'all there