Like most of the UK, universities were surprised by the timing of July’s general election. They had no time to influence the incoming Labour government’s policy commitments.

Labour’s manifesto acknowledged the financial problems suffered by England’s universities, which are caused by a real-terms decline in the maximum fee they are allowed to charge UK undergraduates. But it did not explain how they would be resolved.

However, universities have used the summer to sharpen their case. This is detailed in a new report, which is timed to influence the new government’s first budget at the end of October. It calls for a rise in tuition fees, increased research funding and grants for students from poorer backgrounds.

Many of the report’s authors have served as senior ministers and public officials. They have direct experience of the difficult choices made in government.

But the report has been put together by Universities UK, which represents all types of universities. So it seeks more funding for all university activities, and does not help the government make choices between potential investments. The government could, for example, increase student numbers and research funding throughout higher education or concentrate on particular subjects and places.

This is quite different to the new government’s approach. It wants to provide confidence in university finances. Then set priorities for investment and identify how to address them.

The higher education regulator, the Office for Students, has a new chair – senior public servant Sir David Behan – and a new remit. The regulator will switch resources previously devoted to culture wars issues, such as campus debate, towards closer engagement with universities on their financial health.

In parallel, the government is establishing a new agency called Skills England to set priorities throughout tertiary education. This embraces learning in universities, further education colleges and private training providers, both in the classroom and the workplace. These priorities will be part of a broader industrial strategy, which will be finalised early next year.

In its green paper on the industrial strategy, the government highlights the importance of place. By supporting the clustering of industries in specific locations, it wants not only to stimulate economic growth but also to create education and job opportunities in those places. Different regions have strengths in life sciences, advanced manufacturing, digital industries and clean energy, and different types of cultural industries.

This strategy will require alignment of the diverse influences shaping tertiary education. That includes the choices made by students about what and where to study, employers about the use of a growth and skills levy, and local mayors who already fund adult learning and have been promised more powers. The strategy will also include visas for graduate and other migrant workers, which will become increasingly tied to the government’s priorities.

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Some aspects of Universities UK’s report are consistent with this approach. It advocates closer collaboration between universities, colleges and employers in local areas, and joined up funding and regulation to encourage this.

It sets an ambition for 70% of all young people to take part in tertiary education. This contrasts with the last Labour government’s target for 50% in higher education alone.

The report also shows how universities and government could share evidence to set joint objectives. That could enable a more common understanding of the costs and benefits of international students, and the impact of universities in their local areas.

Crucially, the Universities UK report asks the government for more money. The most substantial changes involve raising UK undergraduate fees alongside inflation, reintroducing government maintenance grants for the poorest students, and increasing funding for research.

This injection of funds would be accompanied by a transformation scheme to improve efficiency. But the report does not identify whether that should lead universities and subjects in some places to grow, while others reconfigure and consolidate.

Universities have successfully argued for higher fees on three occasions during the 21st century to date. In 2004, 2010 and 2016, Labour, the coalition and then Conservative governments agreed to raise the maximum fee for UK undergraduates to £3,000, £9,000 and £9,250 respectively.

These changes were backed by income-contingent student loans and supplemented by increasing research funding. On each occasion, governments were persuaded about the benefits of a financially sustainable, globally competitive and expanding university sector. These changes allowed all universities to increase their income and grow.

However, there is now sharper recognition that increasing the supply of graduates and research can yield unequal opportunities and growth.

Analysis of student migration patterns shows the inequalities arising from unfocused growth, including an increasing concentration of highly skilled jobs in particular areas, such as London.

Labour’s manifesto stated that “the country remains too centralised, with the economic potential of too many regions and communities ignored”. So the government may prefer not to invest more in higher education unless it is focused on specific activities and places.

Since July, universities have enjoyed a more engaged and supportive government. The minister responsible for research has announced that the war on universities is over. And his counterpart in education is welcoming international students to the UK. Any increase to fees and funding will, though, incur political and financial costs. That will require ministers to set priorities and make choices.