] Does anyone know anything about how the rectors of London parishes were appointed?

Exactly the same as the country ones.

Or did the church hierarchy control these? Or something else altogether?

About 600 out of the five and a half thousand benefices in England and Wales were "owned" by university colleges and sundry schools; about the same number were "owned" by the church itself, and another hundred or so were owned by the king. The rest were in private ownership. I don't know if there was a concentration of church -owned ones in the cathedral cities- it would make historical sense to have them there, but I don't have figures, sorry.

There's more detail -lots more- in the archives, if you wish to look.