Sometimes in politics there's a tendency for the best of intentions to surreptitiously breed assumptions. So much energy builds up around solving one issue that other problems surrounding it fade into the background, and it becomes easy to assume that everything else is OK.

One of these assumptions is about social mobility. Devastating statistics show that only 16% of students eligible for free school meals go on to university, as opposed to 96% of private school students. Facts such as these are shocking and rightly gather a focus of political will to ensure that children from state schools have an equal opportunity to reach a university that can enable them to fulfil their potential. But in the determination to do this, there can be a tendency to assume that this is the single answer: if only we can ensure that students from a state-educated background have as good a chance of going on to higher education as their privately educated peers, we have pretty much solved it. Job done.

But the research by the social enterprise group upReach busts this comfortable myth. It shows that ensuring young people from less well-off backgrounds get into university is certainly vital, but not a panacea.

Despite doing as well as their privately educated peers at university, for students from state schools comparable academic performance does not mean equal access to the professions – they trail by a gap of up to 15%. And if they do reach the professions, they earn up to £3,000 less. So in terms of social mobility, we cannot afford to assume that a university education is the great leveller.

Why is this? upReach identifies key barriers holding state-educated students back:. Less privileged students have scantier knowledge as to how to go about achieving their ambitions; have been less equipped with the soft skills employers want; have had less access to useful networks; struggle more to build new professional networks; and have generally had less professional experience though work experience and internships.

Of course, many of these elements need tackling deep at school level, but if we are to enable less privileged university students to seize the opportunities they deserve, we need to do something about levelling this playing field now.