A recent Early Day Motion, which was signed by 13 MPs, noted the "total failure of the 1901 census Web site" and urged the Government to undertake an urgent review of the project.
The motion, which was proposed by Edward Davey, Liberal Democrat MP for Kingston and Surbiton, called on the Government to check that the project's budget was realistic.
The Web site's problems have also proved costly to users as a result of "pointless connection charges," the motion added.
Members of the public were unable to access the site for hours on the day of its launch recently, after it received more than one million hits per hour.
The census Web site was unavailable as Computer Weekly went to press although a notice on the Internet predicted that it would be up and running again "over the next couple of weeks".
The Public Records Office site, which features the details of 32 million people who lived in England and Wales in 1901, was designed to cope with up to 1.2 million hits a day. Managers were not prepared, however, to deal with that number of hits hourly, as happened on the day it launched.
A Public Records Office spokesman declined to comment on calls for a government review but confirmed that the site's creator, QinetiQ, is working hard to get the Web site up and running.
He said, "At present the site is available at a number of service centres such as public libraries but it will be available for general Internet enquiries in the next couple of weeks."