Leeds economics is really interesting because they are one of the best departments for applied economics and very much leaders in the movement to correct the idea that when economists' models conflict with reality, they will back their model every time! It would be a great place to study if you have an interest in things like development economics, health economics, etc. but less so if your interest is maths, maths, maths.
York economics is a generally well-regarded department - it is also a place that people like. Occasionally, there is analysis of the most popular clusters of applications which shows that York is one of the most popular, and sometimes the most popular, 'plus 1' for economics applicants who do all Big 4 (Cambridge (or sometimes Oxford), LSE, UCL, Warwick) plus one applications.
Nottingham is a mystery to me as an economics department and a city. It always seems to do well in the economics rankings, though, so whatever they are mysteriously doing they appear to be doing well.
Newcastle economics is very, very business focused to the point that it is rather debatable whether it is an economics department or just some people in a business school who do some economics. If your interest is in business and financial economics, then it would be a good place to go as there will be a lot of opportunities to focus on these things and link to a wider business curriculum but if not, I think you could tire of the business lens being applied to everything. I always think Newcastle must be a nice place to study because the city and the university's position within it, the areas the students live in, etc. all seem very conveniently located and, coming from a city that mainly relies on buses, the Metro is brilliant.
Birmingham economics is very much a good course at a good university. A kind of can't go wrong option becuase it will always be a respectable subject at a respectable university, even though Birmingham is not especially renowned for economics. If you were to randomly select a fairly academic subject and then randomly select an RG university, you would come up with a lot of places like Birmingham economics. I like cities, so I really like Birmingham because it feels like a proper city. The campus is in easy reach of the city centre but still feels like its own separate area and it is enormous, like a Tardis campus, it is impossible to imagine just how vast it is from the outside.