Luke Georghiou, vice-president for research at the University of Manchester, made the comments to Times Higher Education after the publication of the Biotechnology and Biological Sciences Research Council's annual report.
The council's report showed that it funded Manchester to the tune of ?17.8 million in 2009-10, or ?4.6 million more than its nearest competitor, the University of Cambridge.
The data differed from previously published figures for new grants awarded by the BBSRC in 2009-10, which showed that Manchester was awarded ?9.1 million, compared with ?16.2 million for Cambridge.
A spokesman said the differences reflected the fact that it often took "several months" for funding to be paid out to successful applicants. He admitted that there were currently extra delays as the BBSRC transferred back-office functions to the research councils' Shared Services Centre.
Professor Georghiou said Manchester had been first in BBSRC income "for some time", thanks largely to the success of its Faculty of Life Sciences, which spans biological, biomedical and preclinical research.
The BBSRC report also highlights a decline in grant application success rates from 30 per cent in 2006-07 to 22 per cent in 2009-10. This came despite a fall in the number of applications from 2,240 to 1,865.
Universities have been under pressure from the research councils to limit their applications.
Professor Georghiou noted that Manchester, whose success rate with the BBSRC was per cent in 2009-10, already had a system of internal peer review to ensure the quality of bids. "But we don't want grants to go only to well-established people. We will hold back proposals only if we think they aren't good enough, and support them until they are."
Universities could also reduce the number of applications they submit by changing their incentive structures, he added. "In the past, academics have been assessed not only on their ability to win grants but also on the amount of applications they made. We have to try to incentivise success rather than activity."
"We very much favour (demand management) being done by self-control and not by the councils imposing quotas or penalties, at least with their main partner universities," Professor Georghiou said.
Success rates varied considerably in different categories of BBSRC funding. For new investigator awards, aimed at early career researchers, those applicants who were both successful and female rose from 14.8 per cent in 2008 to 41.3 per cent in 2009. But for fellowships, applicants who were both successful and female fell from 6.7 per cent to 1.7 per cent of the total number of applicants, both male and female.
A BBSRC spokesman said the last figure represented just two women winning fellowships. "This reflects the fact that there were fewer female applicants last year than previously, the competitiveness of BBSRC fellowships, and the fact that some female applicants applied for other schemes. Clearly with such small numbers a slight shift could considerably alter the success percentages," he said.
The report also reveals that the BBSRC spent more than ?4 million last year in redundancy-related payments to staff, chiefly as a result of "science-led restructuring programmes" at its institutes.