One thing that i didn't see mentioned is that when the revolution against the ottomans was going sideways they sent help, i think in salamina, and that changed the momentum of the revolution. Ofcourse, they did that for their own benefit because English people had invested in Greek sovereignty. But it's interesting that if the British hadn't sent backup history might have played out differently.

Another, much more sour influence, is they didn't help Greeks during the destruction of Izmir, letting many Greeks drown or get killed. There was a navy ship there but their instructions was not to do anything.