Twitter has grown by more than 3,000% in the last year, according to figures from internet monitoring site Hitwise.
Its share of UK traffic increased about 33 times between February 2008 and February 2009.
The site is growing 25 times faster than Facebook, which grew by 123% in the same period.
Twitter has a long way to go before it catches up, however, as Facebook still gets 52 times more traffic than Twitter does. Much of Twitter's traffic comes from third-party applications or mobile devices, rather than directly through the website, but even once this has been taken into account, Facebook still gets about 20 times more traffic.
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Twitter's UK traffic has now overtaken traffic to the homepages of the UK's major newspapers, including the Guardian, Telegraph and the Sun. Only the Daily Mail homepage is currently beating the micro-blogging site.
Robin Goad, research director at Hitwise said, "One of the reasons for Twitter's success is the 'eco-system' of sites and applications that it has created via its open API. One of the most notable is Twitpic, which essentially allows users to upload pictures to their Twitter profiles."
There was a notable increase in traffic to Twitter after well known figures such as Barack Obama, Stephen Fry and Jonathan Ross started using the site.