Among other things, it is demanding that the UK Parliament is consulted before article 50 is invoked and the formal process of the UK exiting the EU begins.
The organisers say the aim is to help dispel uncertainty that UK citizens living in Europe feel about their post-Brexit future.
They say there is an "absence of any UK government plans or policies" after the 23 June EU referendum.
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This has led to the forthcoming launch of Fair Deal for Expats (www.fairdealforexpats.com) on 14 August in Lauzun, France.
Spokesperson for Fair Deal, John Shaw, said it will represent the interests of an estimated 1.3 million UK citizens living and working in the EU and to be an umbrella for other expat associations with similar objectives.
Fair Deal for Expats was initially formed by a group of UK citizens living in south west France.
They say they have taken steps to create a voluntary unincorporated association compliant with French law and are now speaking to UK citizens living in other EU member states.
One of the first acts by Fair Deal is in relation to the case brought by Gina Miller and a number of other UK citizens.
The UK High Court is being asked to decide whether the UK government may invoke article 50 of the EU treaty or whether Parliament must first pass legislation authorising the British government to do so.
The case will be heard before the Lord Chief Justice in October.
Shaw told this website, "Some of Fair Deal's members have been granted permission to intervene in the case, to ensure that expat voices are heard."
He said: "Our High Court initiative will ensure that the unique legal issues which pertain to UK expats are presented in the proceedings, the outcome of which will directly affect their lives and the lives of their families."
He added, "The UK is a representative democracy. It is therefore right that those elected representatives in the UK Parliament have a hand in delivering Brexit.
"UK citizens who have made the EU their home, many of whom will have families and businesses on the continent, will be affected by the withdrawal of the UK from the EU.
"It is proper that their concerns and rights are considered during this process."
Meanwhile, Fair Deal is focusing on recruiting more members determined to "have a say" in their future and has appealed to British expat groups, task forces, communities and individuals across the EU to contact them.
Shaw said: "The British government has yet to articulate plans for its expats and it's being reported that the UK has not worked out what the questions are, let alone found potential answers to how it will leave the EU.
"It is crucial that we gather information about how Brexit will affect expats across the EU, so that this can be presented in court and provided to MPs, lobbyists and representatives in due course.
"British expats across the EU must speak up now. The more of us that do so, the louder we will be heard. Others across the EU have worked hard to establish groups to deal with the outcome of the referendum. It is crucial that we all unite."
He says British citizens residing across the EU can apply to join the membership and provide information about the issues faced by UK expats.
Shaw said that anyone not eligible to become a member is being invited to offer their support by donating towards Fair Deal's legal and other professional costs.