The case in the Dutch court argues rights of British citizens are independent of UK membership of the EU.
The five claimants hope the judge will refer their case to the European Court of Justice (ECJ) to clarify their rights in Europe.
If the ECJ decides to make a ruling, it could guarantee rights affecting not only the five claimants, but all Britons living in the EU, even after Britain leaves the EU.
The claimants hope the ECJ will rule anyone who had UK citizenship before the official Brexit date of March 29, 2019, should legally retain rights including freedom of movement and the right of residence in EU member states.
The December deal between the UK and Brussels does guarantee some of the rights British citizens living in EU member states will retain after Brexit, including the ability to live and work on the continent.
However, other questions such as free movement have still not been answered and expats are pressing for clarity.
The named claimants are five UK nationals along with the Commercial Anglo Dutch Society (Cads) and the lobby group Brexpats – Hear Our Voice are the named claimants. They are assisted by Jolyon Maugham, the QC behind a series of Brexit legal challenges.
They claim the Lisbon treaty gives “real weight” to the rights of EU nationals and does not tie these to the politics of their home country.
Some of the five claimants in the case, all British nationals living in the Netherlands, say the confusion and speculation around what will happen after Brexit has been difficult for them.
Stephen Huyton, who has lived in the country for 23 years, said he was concerned his children would not have the right to return to work in the Netherlands after they finished university. They are studying in the UK and have British passports.
He said: “Just because the UK voted to leave, it shouldn’t be able to force citizens to give up their rights.”
Mr Maugham said: “Article 20 gives EU citizenship rights to nationals of member states but it is silent on the issue of what happens to those rights if a member state ceases to be a member state.
“Previous ECJ cases have suggested that EU citizenship rights have an independent reality, not just as an adjunct to national citizenship rights.”
He admitted a favourable result could cause an “asymmetry” between Britons living in Europe, and European citizens living in Britain.
A judge has agreed to rule on the case within three weeks.