As of today, (15th June 2017) data roaming charges for all travellers in the European Union have been abolished, as part of the wider project to create a Digital Single Market. The European Commission has produced a couple of useful factsheets (see links at bottom of article) on what this entails. However, as this BBC article explains, customers are still liable for extra charges if they exceed their contractually agreed data usage limits.
As the BBC article also points out, once article 50 has been fully implemented, it will be the up to a future UK Government to decide as to whether the UK adopts these pricing restrictions or not.
Roaming factsheet: TechnicalroamingfactsheetEN
Roam Like at Home FAQs: RoamLikeatHomeEN