There is no doubt that Alan M is the main man - he speaks very much from (local) experience.
To try and save the 40 minute wait, may I suggest "request" H9 south bound if you wish to go anywhere but north and then you could ask for H9 and H3 to Thorpe and then request Ascot not above a 1000ft then onto Burnham not above a 1000ft - as long as they are not on easterlies! (Confused?)
At night they use the runways instead of the Helicopter Aiming Point (HAP).
As Alam M says, get the adrenaline flowing and jump on every arrival/departure with both feet. Be terse (and listen carefully) and planned with your R/T and they will treat you like a VIP -which of course you are!
A tip I learned from the Citation boys (No APU) - take a hand held VHF to await the clearance from "Delivery". It's OK for us in S76's as we can start the engines on the rotor brake and then, when we get the word, we can "rock and roll".
Have fun and you will look forward to LHR with relish - they treated me very well on Christmas Day 2006 when I attacked them from the Channel Islands - the coffee at Signature is good as well - if you have the time!
LHR ATC reinforce the theory that "if you want something done then give it to a busy person" - they are the best!!
Safe Flying - UG