I have never seen a GBBG attack another bird here in Devon, but a few months back I watched a GBBG juvenvile pulling at fish that were trapped in the rolled up trawl net of a boat berthed in the fish quay at Torquay, the GBBG was actually damaging the the net itself, so they must have considerable strength, whilst there were Herring Gulls and a couple of Carrion Crows waiting around to try to get their share they were all keeping a respectful distance and non of them moved in until the GBBG juvenile had left.
I do also sometimes see GBBG catching fish at the weir on the river exe at Millers Crossing Exeter, I see LBBG and Black-headed Gulls doing the same at that location, but I have never seen a Herring Gull trying to catch fish.