More than 60,000 children are on waiting lists to become Scouts, Beavers, Cubs or Explorers.
The organisation behind the movement said the figure had increased by 20% over the past three years.
The Scout Association said it had more volunteers than ever - but many were offering less of their time and some groups had closed as a result.
Some 475,000 children belong to the Scouts in different age ranges, either as Beavers, Cubs, Scouts or Explorers.
More than 100,000 adults volunteer, which the Scout Association said was "more than we have had at any point in Scouting's history", but it also said the demand for leaders was at an all-time high.
"Our most recent census showed that we grew our volunteer membership by nearly 2,000 in a 12-month period," it said.
"However, with the nature of volunteering in the UK changing and more adults offering their time flexibly, more people are needed to run Scouting than ever before."
Chief Scout Bear Grylls said he was proud young people were continuing to sign up to the movement "but to do more, we need more volunteers".
"We still have more than 60,000 young people who want to join and gain new skills but are unable to do so," he said.
The Scouts organisation includes groupings for four different age ranges - Beavers are aged six to eight, Cubs eight to 10, Scouts are children between 10 and 14 and the oldest group for 14 to 18-year-olds is called the Explorers.
One group to have shut recently because of a lack of volunteers was the section at 1st Mobberley Beavers in Cheshire, which had been running for the past 28 years but remained closed from September following the summer break.
Viv Pike, Explorer leader with Knutsford District Scouts, described it as "a great shame".
"Twenty little boys can now not progress from beavers to scouts to explorers," she said.
"There's no option for them to go to any other group - there are waiting lists all the way through."
Since 2017 waiting list figures across England, Northern Ireland, Scotland and Wales have risen from 51,182 to 60,119.
The South East has the biggest shortage of leaders, the Scouts Association said.
Mrs Pike, who has been involved in scouting since 1981, said the situation had "definitely got worse" over her years as a volunteer.
She said: "I enjoy doing it, you get a great deal out of it when you see children getting their badges - I just don't understand why people won't give up their time."
The Scout Association said it was working with parents and the local community to find a team to take the Mobberley group forward.