Facebook has admitted it can be difficult tracking down the fakers. Its move comes as Winslet, fresh from her success at the Oscars, became the most impersonated star with more accounts than Britney Spears, Barack Obama and former vice-presidential candidate Sarah Palin.
Prior to the Oscars there was a spat between Winslet and Angelina Jolie pretenders and a Winslet account was closed after she described Jolie as a "fat-lipped crazy cow".
Although Fakebooking is mostly harmless there have been a number of cases recently where accounts have been used for more sinister means.
Earlier this month 'Heartbeat' actress Tricia Penrose discovered that someone had got in touch with members of her family through a fake Facebook account in an effort to get her telephone number.
'EastEnders' was also a victim when a fake site in the name of actress Kara Tointon gave away "details" of the soap's plot.
Some genuine celebrity Facebook accounts have been deleted as a result of the clampdown.
Actress Lindsay Lohan complained on MySpace that her account had been removed while David Beckham's LA Galaxy account was also reported to have been deleted.