Having prior arrangement with a handling agent is a must when diverting to busy airports like LHR, otherwise you risk landing with no-one attending the aircraft for hours. Even if you do have handling agent you still may wait a very long time for handling due priority being given to non-diverted flights by handling staff available.
Heathrow Director is correct in that airport operator can refuse diversions (except if it's an emergency) if no handling agent has been nominated or no parking available.