Gillian Keegan, UK education secretary, has signalled she will fight any Home Office attempts to cut migration into Britain by driving away overseas students, saying universities were a “hugely valuable” export success.

Keegan, in an interview with the Financial Times, said she wanted to build on the UK’s booming export market in university education, and to expand education export revenues from about £26bn to £35bn by 2030.

“It’s a sector we should be very proud of,” she said. But with 680,000 overseas students enrolled last year, more than the government’s 600,000 target — home secretary Suella Braverman is looking for ways to control migration numbers.

Keegan and Braverman met on Thursday to discuss options, including reviewing the eligibility of overseas students for a two-year work visa and the ability of students on “low-value” courses to bring dependants to Britain, officials briefed on the meeting said.

Keegan said she would help the Home Office root out any abuse of the system, noting the Tory pledge to cut migration levels and saying she wanted to ensure a high-quality “course offer” to British and overseas students.

But she said of the sector: “It’s world-leading, a great advert to our country. We have a strategy which is very much focused on growing the revenue.” The Treasury is also opposing any reforms that will damage universities.

Meanwhile, the government is looking at allowing teachers to qualify through apprenticeships in order to plug staff shortages in schools and realise Rishi Sunak’s ambition of making all children study maths to 18 in England.

The education secretary left school at 16 to take up an apprenticeship at a Liverpool car factory and said opening a similar route for teachers would “broaden the access” points to the profession.

Keegan, who in October became the fifth education secretary in four months, has been a keen advocate of vocational training and argued apprenticeships would tackle labour shortages across the UK economy.

While she stressed the idea was in its early stages, Keegan said a teaching apprenticeship could encourage more people into the career. The government introduced an apprenticeship route to become a medical doctor this year.

“We can get people who have a second career to earn and learn,” she said. “It would also change attitudes to apprenticeships in schools.”

Currently, most teachers in England do a university degree then embark on teacher training. Keegan’s route would provide an option to replace the conventional university route with a degree-level apprenticeship, including on-the-job training.

“If you want to solve the problem of how you teach maths and physics to 18, you don’t necessarily need to have the level that you’re going to solve nuclear fusion,” Keegan said.

Last month, Sunak set out an ambition to extend the mandatory study of maths after 16 in England, in line with the policy of most OECD countries.

Geoff Barton, general secretary of the Association of School and College Leaders, said any new qualification should prepare teachers properly and not be “a means of getting more people through the door by watering down routes into teaching”. 

With the prime minister preparing a major push to tackle economic inactivity, Keegan also said she hoped apprenticeships could encourage people who had left the labour market back into work.

Because apprentices can earn while they train, Keegan said, the qualification could prove an attractive route for older workers to change careers to “community roles” in childcare or mental health support.

Meanwhile, government officials said the Treasury had rejected a proposal from Keegan’s department to expand free childcare to one- and two-year-olds in England — on top of the existing provision for children aged three to four — because of the £6bn price tag.

Keegan said she wanted to make childcare “more affordable and flexible”. The education department has been asked to come up with cheaper options to try to get more parents of young children back into the workforce as part of a wider government “inactivity review”.

Keegan started her career as an apprentice and went on to study a degree alongside work, which she has said was the foundation for a business career that took her to Tokyo and Madrid and, ultimately, to her role as Tory MP for the safe seat of Chichester.

Keegan’s background has convinced her of the need to improve financial literacy for children, saying that the expansion of compulsory maths could provide a platform for the better teaching of financial skills.

The education secretary accepts that many teachers do not have the confidence to teach those skills and they need better training. “Maths to 18 gives us an opportunity to look at what we can do better,” she said.

She added that her own financial literacy was instilled in her by her father, who talked her through the economics of becoming a hairdresser, Keegan’s initial choice of career.

Instead, she secured 10 O-levels at her school, took a degree in business studies at Liverpool John Moores University and went on to work as a senior executive for NatWest and Amadeus, a tech company.

Raised on Merseyside in the 1980s, when Liverpool was run by the hard-left Militant group within the Labour party and gripped by strikes, Keegan attended a comprehensive school in the neighbouring borough of Knowsley where she started developing her political views.

“I desperately think the Conservative answer is the right answer,” she said, arguing that she could see that the leftwing views of Liverpool council firebrand Derek Hatton were not the answer to the city’s problems.

“I wasn’t particularly a Thatcherite,” she said. “I’m just a pragmatist really. Ideology is a luxury, it’s not something that most working people have.”

With the Tories facing possible election defeat next year, some have touted Keegan as a possible leadership contender for the party’s moderate wing: a One Nation Scouser representing a solid southern Tory seat. Keegan voted Remain in the 2016 EU referendum.

She laughs. “I’d never even thought about being an MP until a few years ago. I was a bit overwhelmed about being asked to go into the cabinet. I’ve never even thought of becoming a PM.”

The idea of becoming an MP came when she bumped into Lady Anne Jenkin, a champion of Tory female candidates, at a London theatre during the interval of The Audience — a play about Queen Elizabeth’s relationship with her prime ministers, notably Thatcher.

Keegan did not know much about politics, but went about standing for a council seat and learning about the NHS as a board member: “I basically designed my own apprenticeship to become an MP.”

Additional reporting by Jim Pickard