It is hoped that Crossrail will relieve overcrowding on London trains

The Museum of Immigration and Diversity in Spitalfields is above the proposed route of the high-speed rail link.

Its chairman, Susie Symes, said the consequences could be devastating for the listed 18th Century property.

Transport for London (TfL) said the museum would not be affected, but would benefit from the rail link.

The rail link would stretch from Berkshire to Essex, through tunnels beneath London, but funding has yet to be secured.

The running of Crossrail through this part of east London does not take significant account of our cultural heritage. Susie Symes

If the project goes ahead, it is unlikely to be completed before 2015 - mayor Ken Livingstone said it was vital for London's future prosperity.

The Crossrail Bill is still going through Parliament - and Ms Symes will be giving evidence to the Commons Select Committee on 15 June.

On Sunday, she said: "Crossrail engineers have only just visited the site and they clearly had no idea before of the physical fragility of the property.

"The running of Crossrail through this part of east London does not take significant account of our cultural heritage.

Crossrail benefits

"This museum is a quite extraordinary project and it is vital we educate people about their cultural diversity."

The building, 19 Princelet Street, is already on the Buildings At Risk Register and needs major work to prevent the walls and ceilings from collapsing.

But Transport for London said it would not be affected, but would benefit from the increased numbers of people carried into Whitechapel station by Crossrail and the East London Line.

"The museum will not be affected by the work nor damaged by the tunnelling which will be more than 100ft below ground," a spokesman said.