Section 2 of the EU Referendum Act 2015 deals with who may vote in the referendum - principally they are those who would be entitled to vote as electors at a parliamentary election in any constituency.
Before 1985 British citizens resident outside the United Kingdom were unable to register to vote in UK Parliamentary elections. The Representation of the People Act 1985 extended the franchise to British citizens resident overseas and enabled them to register as ‘overseas voters’ in the constituency for which they were last registered. This was initially for a period of 5 years, but was later extended to 20 years by the Representation of the People Act 1989, and then reduced to 15 years by the Political Parties,Elections and Referendums Act 2000 section 141.
Thus, section 2 of the Referendum Act 2015 excludes from voting in the referendum those British citizens who, in exercise of their EU free movement rights, reside outside the UK and have been resident outside the UK for a period of more than 15 years.
Mr Shindler and Ms MacLennan were the appellants. They are both British nationals. Mr Shindler was born in London in 1921. On his retirement, in exercise of his right of free movement, he moved to Italy where he has resided ever since. His name last appeared in the UK register of electors in 1982. Ms MacLennan was born in Inverness in 1961. In 1987, in exercise of her right of free movement, she moved to Belgium where she has resided ever since. Her name last appeared in the UK register of electors in 1987.
They claimed that the exclusion was an unjustified restriction of their EU law rights to move and reside within the territory of the Member States and separately that the common law afforded protection to their right to vote as British citizens and full members of the United Kingdom.
Giving the Court's decision for refusing the appeal, Lady Hale (Deputy President of the Supreme Court) said:
"We should make it clear that the question is not whether this particular voting exclusion is justifiable as a proportionate means of achieving a legitimate aim.
The question is instead, firstly, whether European Union law applies at all, as only if it does so is there any possibility of attacking an Act of Parliament; and secondly, if so, whether there is any interference with the right of free movement.
Assuming for the sake of argument that European Union law does apply, we have decided that it is not arguable that there is an interference with right of free movement, for the reasons given by the Divisional Court and the Court of Appeal.
We do have considerable sympathy for the situation in which the applicants find themselves and we understand that this is something which concerns them deeply. But we cannot discern a legal basis for challenging this statute.
Accordingly the application for permission to appeal is refused."
It follows that the Court of Appeal's decision stands ......
Court of Appeal:
The Court of Appeal (Civil Division) - Lord Dyson MR, Elias and King LJJ -  EWCA Civ 469 - held that section 2 was not within the scope of EU law but, even if it was, it did not restrict free movement rights of the claimants or other similarly placed British citizens. It was submitted that the court has a discretionary power at common law to declare legislation unconstitutional where it conflicts with fundamental constitutional rights such as the right to vote. That suggestion was rejected - there is no such common law right but note the judgment of Lord Hodge in Moohan v Lord Advocate  UKSC 67,  AC 901 at paras. 32 to 37.
The House of Commons Library published a Briefing Paper on Overseas Voters.
In 2013, the European Court of Human Rights found against Mr Shindler when he challenged the 15 year rule on the basis of Article 3 of Protocol 1 - Shindler v UK  ECHR 423.
Whether citizens who move should retain voting rights in their country of origin is discussed at EU Law Analysis.
The Guardian 24th May 2016
Who may vote in a General Election - Electoral Commission