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.”

Conservative MP Jeremy Lefroy (Stafford) said: “At the moment young people, and indeed everybody in the United Kingdom, can go without a permit to work in 30 other countries – that’s 27 other EU countries and three EEA countries, with the exception of Luxembourg, and after we come out of the EU it will be zero.

“A French person of the same age will be able still to go to 29 different countries – what a difference that is in terms of rights and opportunities.”

Tory former minister Anna Soubry 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.”

The SNP’s Drew Hendry (Inverness, Nairn, Badenoch and Strathspey) said European citizenship was “absolutely key” to enabling people to broaden their horizons.

He said: “Scotland is not foreign to Europe, Europe is not foreign to Scotland, we are Europeans… we should retain our rights and benefits of European citizenship and I hope the Government bench will take that forward.”

Labour’s Wes Streeting (Ilford North) said the biggest losers from the EU referendum were “those people, particularly young people, across the country whose opportunities will become far more limited because the type of Brexit being pursued”.

The motion was approved unopposed.