Quoting from an article in The Times of 24th September, 2016

Expats will be given a vote in the 2020 general election :

“Millions more Britons living abroad will be entitled to vote in the next general election after Theresa May committed to changing the law before 2020.”

“Harry Shindler, a Second World War veteran [and campaigner for expat voting rights] ……said that he received the assurances in a letter from Downing Street dated September 19.”

“The letter from an assistant private secretary to Mrs May said: “Plans to remove the 15-year time limit on overseas voting rights were set out in the government’s election manifesto in May 2015.”

“This will be delivered by means of a government bill once policy details have been finalised.”

“The government said that it was making steady progress on the issue.”

Note: The article is a bit out of date with its figure of 20,000 for the actual number of expats registered to vote, when over 113,000 were registered for the 2015 general election and considerably more (final figures awaited from the Electoral Commission) for the EU Referendum in June of this year.