Second World War veteran, Harry Shindler, who now lives in Italy, and lawyer Jacquelyn MacLennan, who resides in Belgium, have launched an appeal after losing their High Court battle.
In section 2 of the EU referendum Act 2015, it states that British citizens are excluded from voting, if they have been living elsewhere in the EU for more than 15 years.
Many expats are desperate to vote because they fear that a win for the Brexit camp will mean they have to leave the EU country they currently live in or that it will seriously disrupt their lives. They say it could mean losing their status as EU citizens and they could become "resident aliens" unprotected by EU law.
There are approximately two million Britons living and working in other EU countries and will be impacted by this ruling.
Mr Shindler and Ms MacLennan's lawyers argue that this law prevents many expats from participating in this important democratic process, which may deny them the very EU rights which they rely on every day.
The government has pledged to change the "15-year-rule" in the Queen's Speech to Parliament after the 2015 election; however these changes will not apply to the 2016 UK referendum, held on June 23.
In a recent interview, a British government spokesperson said: "The franchise for the EU referendum is based on the current franchise for UK Parliamentary elections. Currently, British citizens living abroad are entitled to be registered to vote in UK Parliamentary elections as overseas voters for up to 15 years, if they were previously registered to vote in the UK before moving overseas."