A Downing Street petition is calling for the UK government to drop Microsoft's Internet Explorer 6 (IE6) and move to a more modern browser.
The petition says that IE6 has security flaws and uses outdated technology, creating a burden for developers.
The petition comes as the Department of Health advised the NHS to move away from the old browser.
Other government departments - and many firms - still use the software, which was first released in 2001.
"Most creative and software development companies are forced by government department clients to build websites for IE6 when most of the industry has moved on," the petition reads.
"Upgrading would be a massive task for government, but if the public is encouraged to lead the way and the government follows, that would create the momentum needed."
The petition was set up by Dan Frydman of web firm Inigo.
A campaign in the US, called ie6nomore, is supported by more than 70 web firms and claims the software is "holding the web back".
Microsoft has released two more versions of its web browser since IE6, but some firms and government departments still use systems that require it.
It is the latest move in a campaign to do away with the old browser, which gained momentum recently when Google revealed that the browser had been the weak link in a cyber attack on the firm.
Google threatened to withdraw from China following the "sophisticated and targeted" attacks, which it said originated in the country.
The move prompted the French and German governments to advise their citizens to switch to a different browser - such as Firefox or Google Chrome - until the hole had been closed.
The UK government initially downplayed the threat.
Its view was reinforced by Lord West of Spithead, following a question tabled by Lord Avebury in the House of Lords as to whether the government would encourage public sector users to switch to another web browser.
"There is no evidence that moving from the latest fully patched versions of Internet Explorer to other browsers will make users more secure," said Lord West.
"Regular software patching and updating will help defend against the latest threats."
However, the Department of Health Informatics Directorate has issued a statement saying that NHS computers should be upgraded to IE7 as soon as possible.
Microsoft patched the hole in IE6 in January, three weeks ahead of its normal security updates.
It is the latest blow to the venerable old browser. In late January, Google said that it would begin to phase out support for IE6.
The firm said from 1 March some of its services, such as Google Docs and Google Sites, would not work "properly" with the browser.
The search giant has said that it will then phase out support for the browser with some of its other services, such as Gmail.
Microsoft has said that it will support the browser until 2014.
New figures suggest that IE6 is beginning to lose market share and is no longer the world's most popular browser.
Analytics firm Net Applications says that IE6 has now been overtaken by the latest version of the software, IE8, as the most popular browser in terms of market share.
IE6 now accounts for 20.07% of the browser market compared to IE8's 22.31%.