The scheme involves will writers from Co-operative Legal Services talking to customers about leaving a gift to charity in their will.
The new figures, published by the charity and its corporate partner today, predict legacy giving through the scheme will raise nearly £20m in 2013.
Based on figures since it began in June, the joint initiative is projected to raise £65m a year for charities by 2015.
The Co-operative said that before the partnership the number of people leaving a legacy through its will-writing service was negligible, but it has seen a marked increase since its launch. It declined to confirm the number of people who had decided to leave charitable gifts in their wills under the programme on the grounds that it was commercially sensitive.
Rob Cope, director of Remember A Charity, a consortium of more than 140 charities working to encourage legacy giving, said: "This is a fantastic example of how we are achieving results that no single charity can do on its own.
"The next phase of our campaign will focus on building on these partnerships to encourage more like-minded organisations to have the legacy conversation with their customers and supporters. This is the key to growing the legacy market and, in turn, each charity’s cause."
Ian Mackie, sales and marketing director of the Co-operative Legal Services, said: "Since launching this initiative we’ve noticed a significant uplift in the number of people leaving a charitable donation in their will – indeed, many people hadn’t even thought of it until we discussed the options, and they were keen to rectify this."
Research by Remember A Charity, released in October, found 39 per cent of professional will writers discuss leaving a gift to charity with their clients.
Mackie said this showed a huge missed opportunity to encourage legacy giving.