Some 659,030 people submitted applications by the end of June - up 4% on the same point last year.
The final deadline for candidates applying through the University and College Admissions Service (Ucas) was 30 June.
After that, unfilled places are allocated through a post-results process known as clearing.
The latest Ucas statistics show a rise in applications in England, Wales and Scotland of 3%, 2% and 3% respectively. In Northern Ireland the numbers have remained static.
Applications from other EU students rose 5%, while those from non-EU overseas students were up 6%.
The figures also show that, in general, more women have applied than men.
Director of fair access to higher education Prof Les Ebdon said: "These figures are excellent news.
"Applicants are clearly recognising the advantages of higher education and are embarking on a potentially life-changing journey.
"At the same time, our economy and society will continue to benefit from a consistent supply of highly-qualified graduates."
Chief executive of university umbrella group Universities UK, Nicola Dandridge, said: "It is encouraging to see the numbers applying to university increasing again this year, demonstrating the widespread recognition of the importance of a university degree and the positive impact it has on people's lives and the economy.
"The opportunities afforded by higher education are not just there for young people, but also for people of any age.
"It is therefore particularly good to see an increase of nearly 9,000 more mature students compared to last year.
"We are a knowledge-based economy and rely increasingly on people to develop their skills throughout their lives."
Rising numbers of students have applied to start university courses in the UK this year, data shows.