It depends. The Russell Group is a membership group comprised of most, but not all, of the highest ranking universities. It's a marketing tool that has been given more meaning than it should by the general public.
At the individual student level it is perfectly possible to be successful having studied at a non-RG, or more accurately, a non-high ranked university. There are also courses at non-high ranked (non-RG) universities that are outstanding, particularly some vocational courses.
However, at the aggregate level, there is now all kinds of tracking data (from the Higher Education Statistical Agency, HMRC tax data, Labour Force Survey, the collective Longitudinal Educational Outcomes dataset, etc.) that allows researchers to follow all students / graduates or very large cohorts of them across their time in university and throughout their careers. So actual data, rather than individual anecdotes.
It also allows researchers to control for various background characteristics, such as social class. Even when controlling for these things (although obviously the relationship is much stronger if you don't control for them because there is a strong relationship between things like social class and prior schooling experience and the university you attend), this data does show:
- High ranked universities have higher entry requirements. They also tend to attract staff with more ongoing research interests. This means they may, but not necessarily, teach at a higher level, preparing their students better for some jobs. This is quite subject dependent, but from my own experience it is true of mathematical courses, for example.
- Higher ranked universities have more money to spend on student support and facilities.
- They also have more money to spend on staffing, so student : staff ratios and class sizes for things like labs and tutorials tend to be smaller at higher ranked universities.
- When comparing on a subject basis (so, e.g., all history graduates at all universities), the students who graduate from the highest ranked universities are more likely to get graduate jobs immediately after they graduate and to have a graduate job early in their careers. They are also more likely to have a higher level managerial or professional job during their career and they are less likely to experience involuntary unemployment.
- Likewise on a subject comparison basis, graduates from higher ranking universities earn more on average across their careers and at every decile stage of their career.
- Graduates of higher ranked universities are more likely to say that they are working in a job that is appropriate for a person with their qualifications and that uses their skills. They also have higher levels of job satisfaction and general satisfaction with their lives.
So, if you want to play the odds, your odds of having a positive outcome from your university experience will be improved by attendance at a higher ranked university, most, but not all, of which are Russell Group universities.