Many well-known employers have already finished their graduate recruitment for this year, or closed off their application process early on.
Overall, there were an average of 46 applications for every graduate vacancy this year, compared to 51 last year, according to the study by High Fliers Research.
In 2008, before the recession, there were 35 graduates competing for each job. Consumer good companies received 160 applications for each job this year, while media firms received 110.
The report also suggests tough competition among graduates hoping to work in banking and finance or the oil and energy fields, with these industries receiving 84 and 74 applications for each opening respectively.
The study, which looks at graduate vacancies and starting salaries among 100 leading employers, found that these firms have increased the number of vacancies on offer by 4.6% more than expected.
Half of the firms questioned said they had expanded their graduate recruitment this year, with 24 offering at least 20 extra jobs compared to last year.
Martin Birchall, managing director of High Fliers Research, said: "It´s great news for the ´Class of 2013´ leaving university this summer that graduate recruitment at Britain´s top employers is now at its highest level for five years and that many of the country´s best-known organisations are set to expand their graduate vacancies even further in 2014.