<<Er, guys - it was (apparantly) a MAYDAY. Remember that hydraulic failures (more often than not a loss of hyd oil) can affect the flying controls, so a diversion would be made to the nearest suitable runway. There may not be time to fly to Brize, and certainly not all the way to Scotland!<<
Unless the KC is vastly different from civil 707's - I seem to recall that the 707 didn't have much in the way of hydraulic flight controls other than the rudder boost and the flaps, and they were no trouble to extend on the electrical system, the rudder boost was only a problem if one had lost an engine.Dutch roll was hardly a problem at low levels.
The only speed increment I could find when quickly looking through my old flight manual was a 15kt increase in Vref if the LE flaps hadnt extended - and that was on a 320B/C with full span LE flaps - most of those old KC's I've seen only have the LE flap/slat between the engines. Providing the reversers work stopping was not a problem.
Which brings us back to the original question - why LHR? - unless of course the P1 was an AF reserve pilot and in his other life was more familiar with LHR than other UK airfields.