Generally not much, although it depends somewhat on the field. For investment banking the "target universities" for recruiters are quite well known and it may be hard to get in initially if you aren't going to one - however moving into the field laterally after graduation with relevant work experience is still possible. Some fields, such as most clinical roles in the NHS, don't care at all where you studied (and certain stages of recruitment may make it impossible for this to be factored in anyway, e.g. foundation post recruitment for graduate medics is done by computer and where they studied is not and could not be factored into this).
Outside of those exceptions, for most companies recruiting in most sectors, relevant work experience will be the most important thing and where you studied won't count for much if at all. Of course it may be easier at some universities to get that work experience due to industry connections, but it is not the case that only "highly ranked" universities, or Russell Group (which should be obvious that it has no relation to this but...) universities have these connections, especially in technical fields (e.g. engineering, computing, etc). Realistically for the modal graduate where they studied isn't going to make much difference in their employability.