The legal challenge, brought by World War Two veteran Harry Shindler and lawyer Jacquelyn MacLennan, was made after the pair lost their application for a judicial review last month.
Under the law UK citizens that have lived abroad for more than 15 years are not entitled to vote.
Nearly 1.2m UK citizens live in the EU's other 27 countries, while over 5m Britons live abroad in total, indicating that they could have a huge influence on the result.
The vast majority of them, according to polls (and as you might expect), support the UK's continued membership of the EU.
In April the two expats lost their legal battle, meaning Britons who have lived abroad for 15 years or more will not get a say.
They had argued that the law had restricted their right to freedom of movement under EU laws, and that the referendum directly affected them.
But judges ruled that the 15-year rule did not restrict their rights, causing them to take the case to the Court of Appeal. That court has now ruled that "the common law right to vote does not take precedence over an Act of Parliament".
Particular expat referendum concerns surround potential changes in the healthcare and pensions provisions, that come with being a member of the EU, for example whether the state pension provisions will be "frozen".
The UK paid more than £670m to EU countries for Britons' healthcare in the year ending March 2015.
That's under the European Health Insurance Card system, whereby countries can claim back health costs from other EU countries if their citizens use medical services abroad.
Visa concerns and the potential to need to apply for residency are also considerations, as were reductions in income if the exchange rate lowered.