Bear in mind they may well set offers above the minimum level, getting an offer and achieving it aren't the same thing, and yes the overall "prestige" of the university which may well derive from one or two departments can "elevate" the perception of the university on the whole - there are many such examples. Equally there are a few universities which are well regarded overall and have quite a few "standout" departments, but have one or two that are below par. But certainly, entry criteria only really correlate to the popularity/competitiveness of the course, outside of Oxbridge, and maybe one or two other departments/courses. That said, I'm not really aware of any courses outside of Oxbridge who would rather not take a full cohort, than take some with weaker backgrounds, which tells you a lot about entry criteria (and university priorities Re: students).
However as noted, Warwick is frequently compared to Oxbridge because its Maths department is broadly on par with those (and Imperial's) Maths departments. This of course says nothing about the rest of the university...other examples include UCL, which is pretty generally well regarded, and has some particularly strong departments (for example Archaeology or Architecture) but also some quite weak ones (Engineering is frequently cited); Exeter has a pretty good Physics course/department, but the rest of CEMPS is a runaway dumpster fire, and a lot of its other departments struggle to distinguish themselves from mediocrity. Southampton has excellent Engineering, Ocean/Earth Science, and Chemistry departments (the former two certainly being on par with the top 10 if not top 5) , but it's "social sciences" suite (including Economics and Politics) are pretty average at best. If you judge all universities by only their best courses, which you aren't applying to, inevitably you're likely to be disappointed.
Essentially, if you don't want to go into banking, stop thinking about the name of the university and start thinking about what the course actually teaches, and what current students think of it perhaps, because that's what's going to be primarily relevant to you...