One-quarter worries social networking affects their children's real-world social life.
Leading social network Facebook has almost half a billion monthly mobile users, while its rival Twitter has around 60 million users, which both span across all demographics.
However, 59 per cent of British parents are concerned that their children aged between ten to 16 spend too much time using social media and 26 per cent are worried that it will affect their real-world social skills, according to MyVoucherCodes.co.uk.
48 per cent worry who they're talking to, which 43 per cent fret over cyber-bullying, and given that 41 per cent of American teens are bullied via mobile, there's every chance it could happen to British kids too.
Embarrassingly, over two-thirds admit they are clueless how much time their offspring spends on the platform and 53 per cent put this down to them owning smartphones.
Mark Pearson, chairman of MyVoucherCodes, says: "It's not all that surprising to hear that parents are concerned about the amount of time their kids are spending on social media, however it was interesting to find out how many of them think that this is having an effect on their social life offline.