A recent survey has found that 37% of Brits travelling to other parts of the EU turn their phones off due to current high roaming charges.
Nearly half stated they would never use mobile internet in another EU country while 9 in 10 said they avoided using Facebook and Twitter when abroad.
But it is not only tourists who are facing these high costs, businesses are also paying millions a year to stay connected during trips overseas.
Commenting, Lib Dem MEP Catherine Bearder, said:
"There's been a great deal of progress in reducing mobile roaming costs in the EU, including a 91% cut in the cost of using data abroad.
"But this survey shows that there is still a long way to go and that many people are still concerned about soaring phone bills when they get home.
"Liberal Democrat MEPs are now fighting to get rid of roaming charges in the EU altogether by 2015.
"That would be good news for the millions of British tourists who visit Europe every year, as well as the many local businesses that rely on trade with the EU and so regularly travel there.
"And because so many people are hardly using their mobiles abroad at the moment, mobile phone companies could actually end up benefitting too."