John Rowland wrote:

As others have said, TfL maintains all 6000-ish sets of lights on public
roads* in London. It directly controls about half of these from a central
computer system, which coordinates adjacent sets of lights, alters timings
according to time of day, day of the week and so on.

The remaining sets are autonomous, but TfL does set up the phases and
timings and can alter them (on site) as required.

Peter

* ie those where the highway authority is TfL, one of the boroughs or the
City of London. There are a few roads in London where the highway
authority is none of these (eg in the Royal Parks) and if there are any
traffic lights on those, I'm not sure who controls them.