Growing up I was always taught how revolutionary the American government was, but never really thought about it since it was what I had always known. After living here in London for a while I see just how different it is.
There is a recursive nature to the U.S. government. There is the federal constitution, and all the states have their constitutions, and for the most part the power structure follows the a similar path (e.g. The executive branch having similar powers just at a smaller scale: president, governor, mayor).
The U.K. works on something they call a living constitution. Basically, any new laws rule out old ones. This means that if there have not been any laws passed in a certain area for a while laws can date back a few hundred years. The way the power is structured makes it pretty obvious it has been slowly built up over the last thousand years with what just works. So guilds still have some sway and there has only been a mayor in London for the last 10 years or so. Weird stuff can happen like London has two different police forces. MET watches over most of London except the borough of London City which has its own police force just for that small area.
The Greater London Authority is the name given to the power structure for London. Different boroughs have different levels of power depending on how big those villages were before they were swallowed up by ever growing London. ( Can't say the city of London because London city is one of the oldest boroughs) Even the boundaries of greater London are something people have trouble defining. It seems like the greater London Authority just has less and less power the further the borough is.