Students who are the first in their family to go to university should be given a year’s free tuition to allay fears about graduate debt and encourage them to continue into higher education, according to a report.

The authors want the government to introduce a “first-in-family allowance” which would cover tuition fees for the first year of an undergraduate degree – which normally costs £9,250 – for any student whose parents have not had tertiary education.

Parental education can be a big influence on a young person’s decision about whether to go to university, the report by the Higher Education Policy Institute thinktank says, and parents may be more anxious about tuition fees and graduate debt than their child.

“By making the first year of post-18 study free for any student who is among the first generation of their family (and applying this to first-born children and their siblings), we are signalling the importance of overcoming this barrier to educational attainment,” it says.

It is one of a number of recommendations in the publication Making Universities Matter: how higher education can help to heal a divided Britain. The document aims to address the government’s “levelling up” agenda. It also calls for research funding to be redirected to “left behind” regions and the establishment of a national skills council for England, made up of leaders from colleges, universities and funding agencies, to encourage local collaboration to address skills shortages and educational disadvantage.

Rachel Hewitt, Hepi’s director of policy and advocacy, said: “Recent years have shown that some universities are not as closely attuned to their local communities as they thought they were. At the same time they have been subjected to unprecedented levels of policy change by government, which has led to challenging competing priorities. This report provides a road map for universities to get back in touch with the places where they are based.”

Meanwhile, the universities regulator for England, the Office for Students (OfS), has launched a review of higher education admissions, which could lead to scrapping personal statements and the introduction of post-qualification applications, so students apply to university once they receive their A-level results.

Among the areas for consideration is the vastly increased use of unconditional offers, the accuracy of predicted grades, the deployment of incentives by universities trying to market their courses, and the value of using contextual information in admissions for students from disadvantaged backgrounds.

One option is to keep the current system with limited reforms to improve fairness. More radically, the OfS is considering a system where students would continue to apply before their exams, but offers would only be made after they received their results, and a third model where students might register their interest in a university but delay their full application until after their results.

Sir Michael Barber, chair of the OfS, said: “There is widespread recognition that certain aspects of the current admissions system are not working, and may be especially unfair on students from disadvantaged backgrounds. This is fundamentally an open consultation and a genuine attempt to seek views from as wide a range of respondents as possible.”

The universities minister, Michelle Donelan, said the admissions process should be transparent. “It is clear some practices, such as ‘conditional unconditional offers’, can limit the opportunities and outcomes for some students and changes are needed. The OfS’s admissions review will be instrumental in helping assess how the system can be improved.”

The OfS is particularly keen to get the views of past, present and future students, as well as parents, academic staff, higher education leaders, schools and colleges. The consultation ends on 21 May.