Figures suggest some 127 different universities or colleges are offering places on law courses, 76 for maths, 48 for physics, 78 for chemistry-related subjects and 191 for courses relating to engineering.
In many cases, vacancies are intended to appeal to students who may have narrowly missed out on their original offer or are looking to “trade up” to a better course.
Ucas said 154, 000 students were eligible for clearing – up by 8, 000 or six per cent on last year.
It represents more evidence of mounting competition between institutions to recruit students following the introduction of government reforms giving them more powers to expand.
They can take unlimited numbers of students with good A-levels – an A and two Bs or better – as well admitted up to 30, 000 more candidates with lower grades.
The move has already led to some universities resorting to “sales gimmicks” to attract students, with some institutions offering cash awards of up to £10, 000, lap-tops, tablet computers and cut-price accommodation for those accepting places.
Mary Curnock Cook, chief executive of Ucas, said demand for university was as high as ever, despite a slight fall in the number of 18-year-olds in the system.
“The headwind of a decline in population is not getting in the way of growth, " she said.
But John Cridland, director general of the Confederation of British Industry, warned teenagers not to jump into higher education without considering the alternatives.
“University is a passport to success for many young people and graduates are in high demand by employers, ” he said. “But there are other equally successful routes to a great career – including high quality apprenticeships – and we know that ‘earn while you learn’ options, which provide top-quality training and avoid tuition fees, are increasingly attractive."
Jonathan Simons, head of education at the Policy Exchange think-tank, said: “With more places available at university, there is more choice than ever before for those getting good A-levels.
"But universities that have spaces left should do better than gimmicky promotions with free iPads, and start to think more seriously about how to market themselves more competitively – including lowering their fees, and creating different types of courses.”
According to figures, almost 400, 000 students accepted university places before A-level results day – a record high.
Ucas said a further 104, 000 students were still waiting to have places confirmed by Thursday lunchtime.
Another 154, 000 students are already eligible for clearing.
A spokesman said around 35, 000 courses were available on the Ucas website. Each course has at least one vacancy, although many will have more.
Russell Group universities such as Birmingham, Cardiff, Glasgow, Leeds, Liverpool, Manchester, Newcastle, Queen Mary College, Sheffield, Southampton, Warwick and York were among those showing vacancies.
But Roderick Smith, director of admissions at Birmingham, warned that many of those being advertised were already full, with the Ucas website taking time to update.
By Thursday afternoon, Ucas suggested Birmingham had vacancies on more than 200 courses, but he said only two disciplines – history of art and modern foreign languages – were still recruiting.