Apparently not, according to the government's own statistics, though with the pronouncements of senior Tories, including Cameron and Hague, you'd think it was a major problem. These guys are just running scared of UKIP and pandering to the UKIP message. Read this analysis of the figures for immigrants on benefits and make up your own minds.
http://www.newstatesman.com/politics/2013/03/how-ministers-are-scaremongering-over-benefit-tourism
http://www.newstatesman.com/politics/2013/03/how-ministers-are-scaremongering-over-benefit-tourism