Today’s school-leavers are enjoying “the best time ever” to take their pick of university courses, thanks to fierce competition between institutions recruiting from a shrinking pool of 18-year-olds, according to the UK’s university admissions administrator.

Ucas, which operates the admissions process for undergraduate courses, said nearly 98% of applicants received offers of a place to study for a degree this year, and that could be even higher next year as the demographic dip among British school-leavers reaches its lowest point.

“Considering the likely impact of the further decline in the 18-year-old population, and the expansion of applicant choice in the admissions process, now may be the best time ever for students to realise their higher education ambitions,” Ucas said in its review of 2019 application statistics.

The figures lay bare the intense scramble among universities relying on undergraduate tuition fees. The analysis by Ucas showed that most universities extended offers to more than four out of every five applicants, while even those institutions requiring the highest A-level grades were not far behind in all but the most prestigious courses.

A record rate of 34% of UK 18-year-olds entered higher education in 2019, a total of 241,515. Of the remaining 66%, many are likely to enter higher education before they turn 30, based on current trends.

Clare Marchant, Ucas’s chief executive, said the figures “show the unprecedented opportunity for anyone currently thinking of applying to university to be ambitious with their choices. The trends identified through our analysis are very likely to continue into this year, with universities, colleges, and schools continuing to support students from a variety of backgrounds.”

Many students took advantage of the “buyer’s market” by using Ucas’s post-results clearing service to hunt for improved offers, with 73,000 applicants – more than one in eight – finding places. Thousands took advantage of a new option to “self-release” from previously accepted offers, many in hope of finding a more attractive choice.

Students with predicted A-level grades of AAB or ABB were the most in demand overall, with an 87% likelihood of receiving an offer from each university to which they applied. About 39% of applicants received competing offers from each of their maximum of five choices.

Ucas’s end-of-cycle analysis noted that universities have expanded their use of contextual offers to attract applicants from disadvantaged backgrounds. But it found that only 17% of the most disadvantaged applicants reported receiving one, while others remain unaware of their use.

Geoff Barton, the general secretary of the Association of School and College Leaders, said Ucas was wrong to suggest teachers should do more to “familiarise” themselves with contextual offers.

“This is easier said than done. Ucas itself acknowledges that contextualised admissions practices vary substantially between higher education providers. And schools and colleges have suffered years of real-terms cuts which means they are simply unable to provide the level of student support that they would like to be able to offer,” Barton said.

Barton also noted the “worrying decline” in applications to study mathematical sciences, which has been attributed to the tougher maths curriculum in England and fewer students taking the subjects at A-levels.

“It is hard to escape the conclusion that some students have been put off maths by the difficulty of the new so-called ‘big, fat’ maths GCSE,” Barton said.

“We hope the decline in entries turns out to be a blip but it is important the government reviews what has happened and addresses any problems. A decline in maths undergraduates stores up problems for the future.”

Ucas also revealed that demand for places on nursing courses has recovered after the government’s 2017 decision to scrap bursaries. In 2019 a record 30,000 students accepted places on nursing courses across the UK, including 23,000 from England.