Having had the dubious pleasure of having important & immovable business reasons (I was told) to be in that there London during visits to said place by the last four holders of POTUS office, all I will say as a 100% guaranteed prediction that no matter what airport in the bottom right corner of the country you may be trying to transit through, YOU WILL BE DELAYED at the pleasure of the fabled AF1 callsign, no matter if you or they are arriving or departing and no matter what airport they intend to use. Adding the blue silver and white dumbo (I'm not a 747 fan....) into the normal mix of extremely busy traffic just can't help but cause chaos.
My advice is that if you have no alternative to travel via one of the London airports as a POTUS visit starts or finishes, your best option, even if going longhaul, is give up and walk.