Roaming charges, which are added by mobile operators for calls, texts and internet browsing when phone users are abroad, will be abolished from 15 June.
It means UK travellers can use their regular allowance anywhere in the EU.
But Which? warned exceeding allowances would still be chargeable while roaming territories varied between companies.
It said different providers included different countries in their roaming territories, such as the Channel Islands and Switzerland.
Exceeding agreed minutes, texts and data would still be charged in the EU as it would in the UK, with providers charging different rates, it added.
“Many will reap the benefits of these changes and will no longer be put off from making calls abroad,” said Alex Neill, Which? managing director of home products and services. “However, it is important that you take a close look at what is or isn’t included in your current mobile deal. Not knowing what’s included could lead to some surprising charges on your next bill.”
The Roam Like Home legislation is aimed, in part, at preventing consumers being caught out by huge bills when downloading films or other data during their European holidays.
There have been a number of cases when mobile users have been landed with bills for hundreds of euros or pounds.
Critics of the ban suggest the loss of revenue for mobile phone companies could push up prices in general, including prices for non-travellers.
There have been lengthy negotiations between EU officials and the mobile phone operators over the ban.