We could well lose free mobile roaming, but it is hard to give a definitive answer at this stage.
If the UK leaves the EU on 29 March 2019 with a withdrawal agreement in place, then it will not happen immediately. All EU rules and regulations, including on free mobile roaming anywhere in the EU, will continue to apply until the end of the transition period, on 31 December 2020.
It’s also possible that the transition period could be extended, but that’s fairly speculative at this stage.
So what will happen to free mobile roaming once the transition period is over?
Well at that point, EU laws will no longer apply to the UK and UK mobile network operators will be able to reintroduce roaming charges if they so wish. Some major operators say they currently have no plans to do so, but that can’t be guaranteed and it’s bound to be affected by the commercial decisions taken at the time by both EU and UK operators.
It’s also possible that the UK government could create its own laws regulating roaming fees after Brexit. But we don’t know if it would, and even if it did any such law would probably have to take the form of an agreement with the EU. In other words, it would depend on a future UK-EU future trade deal that has yet to be negotiated.