The city of London has it's own police force called the Meltropolitan Police (the Met). This is a different organisation to the normal English police. I think the Met carry guns but the normal police don't.
Rome has a similar thing with the Carabinieri, I understand these guys are part of the military.
The Met is responsible for Greater London (where all the riots seem to be so far). The City of London Police is responsible for the Square Mile (the actual City) in the centre.
The City of London police don't especially carry firearms. That said, you may see more of the specially armed police in the City, simply because of a high terrorist threat
The Met is just another regional police force, similar to (and on a level with) the Hampshire or Sussex police. It is only really special because of the size and importance of its area of operations.
Rome has a similar thing with the Carabinieri, I understand these guys are part of the military.