Glasgow is gridlike; I was there for the Games and it felt like a very un-British street layout. But I don't think anywhere in the UK has grid numbering ("42nd street" etc). We don't do the continental thing of naming streets after significant dates either.
The UK certainly has plenty of surprising road layout, often involving roundabouts, oneway systems, medieval street plans, and roadworks.
I was gonna say that Glasgow city centre is pretty atypical - resembling US cities close enough that a few parts of World War Z (which were meant to be Philadelphia I think) were filmed there. But then I realised that Edinburgh's "New Town" (actually hundreds of years old) is a grid-layout too.
New Town in Edinburgh and the modern city centre of Glasgow both date back to the mid-18th century. They're very unusual for the time insofar as they had a large plan for a large area.
The UK certainly has plenty of surprising road layout, often involving roundabouts, oneway systems, medieval street plans, and roadworks.