Speaking at the Charity Finance Directors' Group annual conference, Peacock - who leaves the commission in three weeks - said it was, paradoxically, more difficult to stop being a charity than to continue to be one.
She proposed a six-month amnesty during which the process for charities to be removed from the register and have their assets distributed to similar charities would be streamlined.
Deregistration is thought to be particularly complicated for charities set up to raise funds for a specific purpose, such as a local swimming pool.
Peacock said that between 10,000 and 15,000 dormant organisations could be taken off the register, which has grown rapidly in recent years to a total of 198,000.
She told Third Sector that she wanted the commission to put resources into a major drive to ensure "all charities proactively want to be charities, rather than just hanging in there by default". A process of education was needed, she said, to explain to trustees how they can deregister.
"It's not that we want to get rid of charities, but the Charities Bill is a good opportunity to put our house in order," she said. "When the Bill is passed there may be even more organisations applying to become charities."
Peacock raised the issue with former Home Secretary Charles Clarke, who was thought to be sympathetic, and said she would bring up the proposal with the new minister for the third sector, Ed Miliband, before her tenure at the commission ends.
Rosie Chapman, director of policy and effectiveness at the commission, endorsed Peacock's remarks. "If trustees feel they have got to a point where the charity is no longer effective, they don't need to feel they are stuck with this millstone of a charity round their necks," she said.
Assets could be given to related charities in the local area or to grant-making trusts, she said.
- See Finance news, page 9.