As Volunteers' Week kicked off today, CSV spokesman Jason Tanner said many of the events organised in the first five months of the year had been oversubscribed.
He added: "There aren't enough opportunities for volunteers. We want prisons, hospitals, schools and social services to think more creatively about how they can work with volunteers."
According to the Home Office, 26 million people volunteer, but research by CSV indicates that a further 11 million are ready to give their time.
Volunteering England, the other organisation behind the Year of the Volunteer, said the programme was on course to increase the profile of volunteering substantially. Chief executive Christopher Spence said significant support from the media and commercial sectors had helped.
He added: "It's always true that there is more to do, but my expectations have been exceeded. There has been a high level of buy-in from outside the voluntary sector. By the end of the year, I expect volunteering to be enjoying a higher profile across our society."
Spence cited ITV and Starbucks as examples of non-voluntary organisations backing the project.
"There has been enormous coverage, and I will be surprised if there is not substantially more volunteer activity as a result."
As part of the Year of the Volunteer, Volunteering England awarded a total of £490,000 to 25 volunteer development agencies to help them respond to increased traffic.
Volunteering England has a total fund of £2.8m to allocate in grants in 2005. The first grants were awarded in April this year. Thirteen smaller amounts were awarded under Volunteering England's small grants programme, in which individuals or organisations bid for grants of up to £6,000.
A poster campaign has been launched, calling on the public to nominate 'star' volunteers they feel deserve a Year of the Volunteer medal. A total of 2005 medals have been produced, and 'regional champions' will be presented with theirs at a ceremony in January.
Volunteering England estimates that 50,000 people will take part in 400 events to celebrate Volunteers Week from 1 to 7 June.