The campaigners say it is wrong they are unable to participate in the vote, which will have a “very real impact on their lives”.
They argue that blocking them from the ballot box on June 23 means their rights under European law are being breached.
“What we are doing here is re-establishing democracy. If we can do that for these two million people that is quite something. Nobody should have the right to get up in Parliament and deny our citizens the right to vote.”
Harry Shindler, campaigner for expat voting rights
If successful, the High Court proceedings could see the In/Out vote delayed while up to two million extra names are added to the register of voters.
Under the EU Referendum Act, British citizens living in the European Union who have been outside the UK for more than 15 years are unable to participate in the decision on Brexit.
The legal action was launched by Harry Shindler, a 94-year-old war veteran who has lived in Italy since 1982, and Jacquelyn MacLennan, a British lawyer who lives in Belgium.