For some charities, that analysis rang true. If you want to volunteer at Crisis next Christmas Day, for example, now is the time to register. The charity regularly has 7,000 applications for only 5,000 places.
Estelle Burns, director of organisational development at Crisis, says it helps that the charity is well-known. "You could say that we almost have more volunteers than we know what to do with because we have a good reputation," she says. "But we have to maintain that reputation, so we are never complacent."
But it isn’t just the big names that attract a surplus of volunteers. The Whitechapel Mission, for example, already had a waiting list for Christmas volunteers last June, when third sector minister Ed Miliband visited as part of his Volunteering Week roadshow.
This type of situation seems a long way off for Kirsty Palmer, Project 50K development manager at Girlguiding UK. "Our experience is the reverse of what Dame Elisabeth is saying," she says. "We have 50,000 girls waiting to join the guide movement because we need another 8,000 volunteers. In some parts of the country, things are so bad that parents are putting their daughters' names down for the Brownies when they're born."
Hoodless admits that not all charities are reaching a volunteer saturation point. "We can only go by our own experience," she says. "We work at the coalface with 200,000 volunteers and 15,000 volunteering partners each year - but parts of the sector have already reached saturation, and other parts are approaching it."
Crisis and the Whitechapel Mission would no doubt like to think their success at recruiting volunteers is simply the result of impeccable management, but Palmer of Girlguiding UK believes other forces are at work.
"There's a prestige attached to volunteering for certain organisations and certain causes," she says. "We are seen as old-fashioned, and people probably see volunteering as something that implies a sense of duty."
Hoodless believes it's not so much the cause as the kind of volunteering that makes the difference. "Research in the US shows that episodic volunteering - where you can just turn up on the day and do something - is more attractive to people," she says. "This is supported by the growth in popularity of events such as CSV's Make a Difference Day and Go London."
This is certainly rings true for Girlguiding UK. Part of the problem it faces is that, in order to be a Guide or Brownie leader, volunteers must make considerable time commitments.
"The pressure of time is a massive thing," admits Palmer. "Women's lives have changed radically in the past 20 years. Rather than have to let people down a few times, they will just withdraw from volunteering altogether."
Girlguiding UK adapted its volunteer strategy to take this into account by launching a ‘12 Hour’ initiative to offer more flexible volunteering opportunities.
"Local groups identify jobs that need doing, such as repainting their hut or providing transport," says Palmer. "We will find a way to accommodate any volunteer with time to spare. People who volunteer want to see an actual result almost immediately - the more people we can get to give little amounts of time, the less time our volunteers will need to commit to us."
Burns attributes the success of Crisis to considering what volunteers want to get out of the experience. "We are obviously providing a service to homeless people, but we are also providing a service to our volunteers," she says. "Some of them do it because they want to give something back, but many would have nothing much to do on Christmas Day if they didn't volunteer - they might even spend it alone."