The report, Treasurehouse and Powerhouse, commissioned by the museum and written by two prominent academics, says that in the long term, the current government grant tied to inflation will not be enough to allow it to compete with private sector attractions that can charge for entry.
The 123-year-old museum, a registered charity, is the fourth most popular free visitor attraction in the capital after Tate Modern, the British Museum and the National Gallery. It attracts three million visitors a year, including 125,000 schoolchildren.
It is funded by a government grant of £38m, and generates an extra £14m through sponsorships and commercial work, making a total turnover of £52m.
But its contribution to the economy, through the money spent locally by visitors, is much bigger. The museum estimates that it contributes £3-£4 to the economy for every £1 of government grant.
The report argues that the museum's academic role is often overlooked as its research takes place in laboratories and offices beyond the public gaze.
"While new resources have been provided in recent years to improve the attractiveness of the institution to visitors, the 'backstage' part of the museum has not enjoyed the same scale of re-investment," it says.
The authors suggest that it could raise awareness of this role by becoming a "much more high-profile authority on current and often controversial scientific issues the public has to wrestle with".
Museum director Sir Neil Chalmers said: "The report does raise some alarm bells and it is now up to us to look at how we can use the information."