A spokeswoman for Camelot, which runs the National Lottery, said it had done "consumer-based, sales-based and econometric research" and believed that the National Lottery was losing £1m a week in sales to the Health Lottery.
About 28p from every £1 National Lottery ticket goes to good causes, but the rate for the Health Lottery, launched in September by the media owner Richard Desmond, is 20p in the pound.
"We estimate that this represents at least a third of weekly Health Lottery sales," the spokeswoman said. "Our analysis shows that the majority of this cannibalisation is being felt by National Lottery draws that take place on a Saturday – the same day as the Health Lottery draw."
She said that after calculating the amount the National Lottery gave to good causes and paid in duty to the Exchequer every year, this meant that £20m could be lost by them. Unlike the National Lottery, society lotteries such as the Health Lottery do not pay duty on sales, she said.
"We expect this figure to rise sharply in the coming months," she said. "The Health Lottery says it plans a number of marketing initiatives and changes to its game plan to ensure it reaches the £50m it promised to raise for health-related charities in its first year."
The spokeswoman said Camelot had shared the figures with the National Lottery Commission and the Department for Media, Culture and Sport. Camelot raised concerns about the Health Lottery with the Gambling Commission last year and asked it to carry out a review then, she said.
A spokesman for the Health Lottery said that since its launch it had raised more than £10m for good causes. The DMCS itself had estimated, he said, that if current National Lottery ticket sales trends continued, income would increase in 2012/13 by about £232m more than it had projected in September 2010.
"We have always believed the Health Lottery scheme, on behalf of the 51 community interest companies that participate, would inject a new lease of life into the lotteries sector, offering consumers choice without diluting the overall market," he said.
"This has proved to be the case and we are delighted that people have recognised the scheme is a fun, new alternative that donates funds directly to local good causes in their areas."