] Does anyone know anything about how the rectors of London parishes were appointed? Everything I can find concerns those in the country. Were these also in the gift of noblemen? Or did the church hierarchy control these? Or something else altogether?

I can't answer your question with any degree of precision. However, my educated guess is that the relevant bishop would decide on parish appointments, in cities and towns where the living was not in the gift of a local landed aristocrat.

I have read all of Anthony Trollope's Barchester Chronicles which deal with some pretty hilarious mid-eighteen hundreds church politics. All of them are set in Cathedral towns and cities as opposed to small country towns. If my memory serves, what I remember from Trollopes book, is that it the local bishop who makes decisions on local church appointments. However, all of his reccomendations have to be approved by the General Synod of the Church of England, to which bishops were answerable.