Ministers have said they would be "very happy to discuss" the prospect of Britons retaining European Union citizenship after Brexit.
The pledge came as Plaid Cymru led calls in the Commons highlighting how many identified as European as well as British, English, Scottish, Welsh or Irish.
The party led an opposition debate on the issue and wrote to Theresa May beforehand urging her to make retaining European citizenship an objective in Brexit talks.
The letter was backed by the SNP, Liberal Democrats and the Green Party, as well as a number of pro-EU groups.
Labour refused to commit directly to the policy, but during the debate shadow Home Office minister Nick Thomas-Symonds said: "We shouldn't be ruling any options off the table."
Immigration minister Caroline Nokes told MPs the Government would be "very happy to discuss the specific issue" with the European Union.
Plaid MP Hywel Williams, a former leader of the party at Westminster, said the move was "just one part of the effort to salvage something from the wreckage of this slow, this very slow motion, disaster".
He added: "European Union citizenship did not replace UK citizenship when it came into force. It is indeed additional.
"Both continue to co-exist, and leaving the EU does not entail the end of EU citizenship for UK citizens.
"This government is, by default, unfortunately, intent on taking away something of significant value to the people of these islands.
"They should not do so. In fact, they should make the retention of EU citizenship an important, sensible plank of future negotiations."
European citizenship allows UK nationals to live, work and study in the 27 other member states, as well as other countries which are members of the European Economic Area or the European Free Trade Association.
Mr Williams said there were different legal interpretations, with some arguing citizenship was a fundamental right that should not be affected by Brexit.
Speaking later in the debate Ms Nokes said: "We are content to listen to proposals from the EU on associate citizenship for UK nationals, however to date this has not been formally proposed to the UK in the negotiations.
"EU treaty provisions state that only citizens of EU member states are able to hold EU citizenship, therefore when the UK ceases to be a member of the European Union UK nationals will no longer hold EU citizenship unless they hold dual nationality with another member state."
After the minister's comments Tory MP Matt Warman (Boston and Skegness) went on to dismiss the comments of Sir Martin Donnelly, former boss of Liam Fox's international trade department, who said that Brexit was like exchanging a three course meal for a bag of crisps.
Mr Warman said: "I don't want to say you can have your cake and eat it, but you can have a three course meal and a bag of crisps.
"I do think it is important to bear in mind that it is always tempting to say if you were on one side of the argument that it will all be brilliant and if you were on the other side of the argument it will all be terrible.
"There is a compromise somewhere in the middle and that is what I think we will be seeking."
His comments were in marked contrast to Tory former minister Anna Soubry who said Brexit was "the stuff of madness".
She said: "It must be the first government ever in the history of our country to admit that a free trade agreement, even if we got what the Prime Minister wants, would actually make this country less prosperous than it is now.
"This is the stuff of madness."