Although commonly described that there were just two US carriers into Heathrow, Pan Am and TWA, with National making a third just to Miami, until they got rolled into Pan Am, there were others that turned up, with a US approach called an "interchange flight". Because Pan Am was basically only allowed international flights, and the US domestic carriers were not for a long period, and because TWA was allowed both, Pan Am in the 1960s-early 70s developed flights that continued as a domestic flight beyond the US gateway, on the route of a domestic airline. This led not only to Pan Am aircraft turning up at US airports they otherwise did not serve, but also the partner's aircraft turning up at Heathrow. This was all well before these carriers managed to get licences to come to Europe in their own right,
There were several such arrangements, each one seemed to be organised differently for who did what share. Aircraft worked through but crews were always changed at the US gateway, the interchange point.
Delta had the longest standing arrangement, from Atlanta to Washington, then on as a Pan Am flight to London. This one seemed to be 6 months of the year by aircraft of each carrier. It lasted probably for 10 years or so, from the DC8 era into the 747, and led to Delta aircraft of both types turning up at Heathrow. At Pan Am the DC8 dropped out of favour early on, but they kept some on and this was one of their last operations, and in fact some of their others, fully kitted out for international operations of course, were sold to Delta and used on the route. Delta didn't have any 707s and thus no crews for it, so the DC8 had to last until the 747 came along.
Northwest had an arrangement through Detroit onward to Minneapolis, which again went back and forth, this one seemed to be proportionalised by mileage so Pan Am aircraft did most but Northwest turned up on it for certain blocks of time. Northwest had 707s properly configured for their transpacific flights to Asia, so aircraft compatibility was not an issue.
Braniff continued the Pan Am London-Chicago flight on to Dallas and Houston. I never encountered a Braniff aircraft at Heathrow (comments ?) so seems to have always been a Pan Am operation. Unlike the others the round trip could not be achieved in a day so it needed two aircraft. Pan Am had a handful of other operations from Houston, not otherwise connected to their network, so it was operationally convenient for them.
There's a lot more to all this, some flights were continued as Pan Am from London to Frankfurt, you could probably write a chapter on all the variations that happened from year to year.