I would say Manchester is not a university you can classify as prestigious. It is just a Top university, just like NYU.
See some of my points here: King’s College London in the US - #30 by LutherVan
You don’t tell people you attended the university and there is an impression of selectivity and “Wow”.
I would put it as one of the top 51 to 150 universities in the world. So still very, very good to attend.