There have been an average of 52 job applications for every graduate position this year - an 11% increase on last year, a study says.
The High Fliers survey of the 2012 graduate market says many of the best-known organisations have finished recruiting for the year, closing applications early.
Applications to the UK's leading employers have risen 25% since 2009.
For the third year running, companies are taking on slightly more graduates.
The study, based on responses from 100 "leading employers", suggests graduate opportunities increased by 0.9% in 2012.
But the 11% rise in applications reflects the large numbers of graduates who failed to find employment at the end of their studies in previous years.
Competition is toughest in banking and finance, at leading retailers, consumer-goods manufacturers and investment banks, where employers received at least 80 applications per graduate post.
The sector with the lowest number of applicants per vacancy is accountancy and professional services.
The survey also said that although there remained a recruitment freeze in many government departments and agencies, graduate vacancies in the public sector were expected to increase by 20% this year.
This is partly driven by teacher-training organisation Teach First taking on 1,000 graduates this year.
Managing director of High Fliers Research, Martin Birchall, said: "It's good news that Britain's best-known and most sought-after employers are defying the recession and have increased their graduate recruitment for the third year running.
"But university-leavers from the 'class of 2012' are still facing considerable competition to land a good graduate job this summer.
"Employers have already received an unprecedented number of applications for this year's graduate vacancies and organisations in several of the most popular career sectors have now filled all their places for 2012 or have closed-off their applications early."