Going to a Russell Group university or not won't make a difference in your employment prospects. They will depend on you and what you do to make yourself employable - graduate recruiters will always prefer someone going to another university who actually made a point of getting internships, work experience, placements, vacation schemes etc, and developed their transferable employment skills through other activities while at uni, than someone who just went and attended lectures and sat exams for 3 years (at a Russell Group uni or otherwise!).
The only exception to that is investment banking and management consulting, sectors which have their own list of target unis. Notably not all RG unis are target unis though and it's pretty much the universities you would expect that are target unis (Oxbridge/UCL/LSE/Imperial/Warwick). Outside of that though as above, it's a non-issue (or rather, you're approaching the issue from the wrong angle!).