Don't believe David Cameron and the Remain campaign

The new regulations on mobile phone roaming wouldn't disappear after Brexit.

'Millions of mobile phone customers with an allowance package will benefit from reduced roaming charges in most of Europe from tomorrow, ahead of the blanket ban on such charges from June next year.

The roaming caps will apply when using your UK phone abroad in any European Union (EU) or European Economic Area (EEA) country – this comprises all 28 EU member states, plus Iceland, Liechtenstein and Norway (but not Switzerland). A full list of EU and EEA member states can be found at Gov.uk.'

More here http://www.moneysavingexpert.com/news/phones/2016/04/cost-of-roaming-in-europe-to-be-slashed-for-millions-of-mobile-phone-customers but obviously not on the institutionally pro EU BBC.