Sky News understands that Citizens Advice is urging the Government and providers to work on a voluntary agreement to stop high bills, which would include more warnings for customers and a voluntary price cap.
The charity said people travelling outside of the European Union face bills of thousands of pounds because of high charges and because they do not realise how quickly costs can rise or even that they are using roaming data.
Citizens Advice chief executive Gillian Guy said: “The market shouldn’t be a lottery where some customers can be unwittingly plunged into life-changing amounts of debt just because they used their phone.
“A voluntary price cap would help better protect customers and companies could do more by giving more warnings to customers if their bills start to rise.”
Within the EU the highest per megabyte roaming rate is capped at 17p, under changes brought in by the European Commission last year.
However, there is no such limit outside the EU, and researchers found the roaming rate per megabyte can be as high as £12.50.
Watching an episode of Eastenders could cost up to £1,360 in Turkey, compared to a maximum of £32 inside the EU, Citizens Advice discovered.
The charity has helped military personnel who were billed for thousands of pounds after leaving their data roaming on while deployed abroad and a holidaymaker who was hit with a bill of £1,500 after turning on data roaming to download an album while in Egypt.
The rate consumers pay depends on which provider they are with, where they travel and whether they have purchased a “bolt-on” which gives them a set amount of data to use abroad for a fixed cost.
At the moment, phone companies are required to send a warning message to customers who are outside the EU when a bill reaches €50 (around £35), asking them if they would like to continue.
But Citizens Advice argues that because there is no requirement to contact the customer again, they can rack up much higher bills without knowing.
Consumers can check their data roaming is off and contact their provider to find out their tariff, but the charity wants companies to do more.
Citizens Advice wants a voluntary agreement which would include standard warnings for customers about how much they were spending on data at regular intervals above the €50 level, and a maximum per megabyte cost.
It also wants to see measures introduced to ensure customers who are given unexpectedly high bills are treated fairly, that money is not recouped immediately and people are not pushed into debt.