Queen Mary’s location is not crappy. It is just unglamorous.
It is not the neighbourhood for the historic buildings and siteseeing many associate with London. I dare say only Queen Mary’s building is of great architectural interest in a 200 metre radius of that area.
The area the university is located at is quite ethnic (heavily filled with people from the Indian sub-continent community). It is not a high crime area but it is not prestigious.
That said, it is not too far from the City & Canary Wharf (the duo-financial centres) and Stratford centre (where the glamorous Westfield Shopping Mall is). The university itself is within 150 metres walk to 2 stations (each located in either direction you take as you leave campus). So if the area is not your scene, you can easily and quickly get out to where you prefer.
Commuters are not a nuisance and the transport links around Queen Mary is actually one of the more abundant in comparison to many other parts of London that are not central.
Queen Mary’s English academics are some of the best and most respected in the UK.
One can even argue, based on performance alone (not prestige), they are currently the next best thing to Oxbridge in the UK:
https://www.researchprofessional.com/media/pdf/UoA29_English_Language_Literature.pdf
So, at worst, they are quite good.
In regards to other schools besides London and Edinburgh, if the universities already named on this thread are not satisfactory, just follow the rule of thumb in the UK that “after the prestigious/top universities 12 or so, the next tier are usually the MAIN universities located in the big regional cities (not already in the 12)”.
So just look at cities like Nottingham, Birmingham, Sheffield etc.
I emphasised “main” because there is a difference between University of Sheffield and Sheffield Hallam University. Same with University of Notthingham and Nottingham Trent University. The former are the ones I am referring to as “main”.