Actually - the "Overseas Electors Bill 2017-19" has been running through parliament - the proceedings were adjourned 10 days ago (22 March) on its third reading - I think they ran out of time;
services.parliament.uk/bills/2017-19/overseaselectors.html
The bill is supported by the Conservative frontbench - but not the Labour frontbench;
www.dailymail.co.uk/wires/pa/article-5427507/MPs-plans-end-15-year-time-limit-expats-voting-British-elections.html
2018 - Ilford South MP Mike Gapes (Labour) who spoke in support of the Bill, wrote on Twitter:“I am appalled that Labour frontbench are opposing the bill and trying to talk it out."
“Clearly in this case Labour Leadership is for the few not the many.”
Labour 'betraying' British citizens abroad who cannot vote.
Refusal to back bill removing time limit on expats’ voting rights angers campaigners.
www.theguardian.com/politics/2018/jun/27/labour-betraying-british-citizens-abroad-who-cannot-vote
Expats have no sympathy from Jeremy Corbyn;
Hansard: Extension of Permitted Period of Overseas Residence
House of Commons Debate 1989;
api.parliament.uk/historic-hansard/commons/1989/jul/05/extension-of-permitted-period-of
Mr.Jeremy Corbyn (Islington, North)
"In a spirit of generosity, I tabled an amendment specifying 10 years. On reflection, I was probably a little too generous.I am sure that the Minister will be grateful for that and will accept my amendment."
"Twenty-five years is excessive in the extreme.People who have been resident abroad, working abroad, earning money abroad and probably not paying taxes abroad are not likely to be interested in politics in this country." "The Government's motive is to find a pool of voting fodder for the Tory party in the tax havens around the world."
"They are not interested in democratic movements in this country, because they have set themselves up in some other country and earn their money there. My 10-year rule would allow those people who have working contracts abroad—for example, those in the diplomatic service—to maintain a link with this country I believe that a period of 25 years is quite ridiculous and, therefore, I commend my amendment to the House."