As a longtime airline postcard collector, I'll take a shot, guessing simply at the names of some supplemental carriers that I'm pretty sure operated back then. I've no real idea whether they operated trans-Atlantic services to London...
Sticking to WHBMs' criteria (LGW in 1969):
U.S. Airlines
Saturn (707, DC-8)
No, STN only IIRC
World (707, DC-8)
Yes
Universal (DC-8)
Not in 1969
Overseas National Airlines (DC-8)
Yes
Capitol (DC-8)
Yes
Modern Air (990)
Yes, but he said DC-8 
Trans-International (DC-8)
Yes
American Flyers Airline (707 and maybe 727)
Earlier but not in 1969
Seaboard (707, DC-8)
No, cargo only to LHR
(If I can think of any more I'll add 'em to this list. Many of the above airlines went on to order and operate widebodied aircraft in the 1970s and beyond)
British Airlines
British Eagle (707)
Donaldson (707)
Invicta (I'm pretty sure this was British but...?) (707)
Yes British, but 720s and not from LGW I think
Canadian Airlines
Wardair (707)
Yes
Add Canadian Pacific DC-8