How exactly is there no reciprocity? The US government hires carriers and airplanes from other countries when necessary. It isn't necessary often because we have such a large supply of available aircraft in our country. But the US government can and does hire foreign aircraft.... most notably Russian Antonovs.
If there were no available US aircraft for a specific trip, and there was an available British aircraft, the US government would hire it. However, due to the large number of available US airplanes sitting around, hiring the Brits isn't the most cost effective solution most of the time, and it hasn't been necessary.
There are not as many available airplanes in the UK. Therefore, they went outside of the UK. That's how things work in a world economy. The US would do the same thing if need be. Don't fool yourself into thinking that it wouldn't.
We have a ton of unused airplanes sitting around in this country, with crews just waiting to fly them. Lots of available lift. That is not true in the UK.