Oxford University has previously announced a drive to attract more of the group.
Nick Hillman, director of the Higher Education Policy Institute (HEPI), which has released a report on the plight of young men in education, told the Mail on Sunday: 'When putting together our report, we were shocked to find so few higher education institutions had these sorts of targets.
"The problem is so evident and we've continued to go backwards."
"Some people oppose this whole agenda - we were told we were wrong to look at gender and should care only about class."
The Institute's report calls for more foundation year courses preparing students for studying a degree as a means of encouraging more young men to apply.
Official figures also point to a growing gender gap in British universities, with 23 out of 149 higher education institutions having more female than male students.
Previous research has indicated that university staff have a mixed reaction to schemes aimed specifically at white boys in case it leads to accusations of racism.
A study led by King's College London said: "We found that people were quite uncomfortable with the idea of running a targeted activity with this group, in a way that we've not encountered, for example, targeting young black African men.
"We had quite a lot of people saying.
"This isn't going to be a white-only event, is it?"
Essex and Aston's initiatives follows a warning by the Office for Students, which regulates universities, in September, that institutions could be punished unless they give a higher proportion of top degrees to black students.
The body plans to set a series of national targets to apply to all universities.