Universities will be allowed to charge students almost £2,000 a year more in fees in return for allowing them to complete a degree over two years instead of three, ministers have revealed.

The decision to allow universities to charge a 20% premium for so-called “accelerated degrees” is the latest attempt to encourage more institutions to offer the option.

It follows frustrations inside government that only about 2,500 students – just a fifth of 1% – are studying accelerated degrees, despite hopes that they would encourage more mature students into higher education, as well as those who do not want to commit to three years on campus.

There has long been support among ministers from different parties to encourage the growth of two-year degrees, but universities have complained that the extra costs of their longer term times and the loss of a year’s tuition fees meant they were reluctant to offer them.

There had been suggestions earlier this year that universities could be allowed to charge the full three years’ worth of fees over two years, which would have seen students paying more than £13,500 a year. However, ministers have opted to allow institutions to charge a premium that they believe will cover any extra costs.

Under the latest proposals, universities will be able to charge up to £11,100 a year in fees for accelerated degrees, compared with the £9,250 paid by regular undergraduates.

The fast-track degrees offer the same qualifications and are quality-assured in the same way as a standard degree. The new fees regime should be in place by September 2019. However, they have to be approved by parliament – which may be problematic for the government when faced with a Labour party determined to abolish fees altogether.

Jo Johnson, the universities minister, said the move was part of the government’s attempts to “bust open the increasingly inflexible system of higher education”. He argued that the average student taking up the shorter courses would be £25,000 better off due to lower overall fees and an extra year’s earnings.

“There are savings for the student, big savings for the taxpayer, and universities have an incentive now to offer these courses, because instead of losing all of that final year of income, they just forgo a proportion of it,” he said.

He said he was confident that universities would now come forward and offer the accelerated courses, and that there would be a “huge first-mover advantage” to the institutions that did so.

The shorter degrees might encourage more mature students to go in to higher education, Johnson said, but the move was not explicitly an attempt to head off skills shortages when immigration controls are tightened after Brexit.

“Over the years, we’ve seen the classic three-year residential model take up an increasingly large market share,” Johnson told the Observer. “We have been concerned by the decline in some areas of provision that we want to give a boost to now – and in particular we have been worried about the decline in mature students looking at higher education to reskill, retrain and adapt to a changing economy.”

A recent government survey found that 73% of higher education providers reported demand from students or employers for the courses, but 36% of responders cited concerns about the cost of delivering them. More established universities were found to be less likely to offer them.

Alistair Jarvis, chief executive of Universities UK, said: “Several universities have been offering two-year, fast-track degrees for a number of years, but demand has been limited under the current system. But if these proposals help encourage even more flexible modes of study, and meet the needs of a diverse range of students and employers, it is to be welcomed.

“The priority is ensuring that each student is given good advice and information so that they can choose the course and university that is right for them. While the three-year undergraduate degree on campus will remain the preferred option for many students, accelerated degrees could also meet the needs of many students and their families.”

Les Ebdon, the director of the regulator Fair Access to Higher Education, said accelerated degrees were “an attractive option for mature students who have missed out on the chance to go to university as a young person”.