Foreign Secretary Philip Hammond has called for early talks in order to guarantee the status of EU nationals living in the UK in the wake of the Brexit vote.
Mr Hammond said he wanted to see a reciprocal agreement with EU counterparts that would also protect the rights of UK nationals in Europe, before the start of formal Article 50 talks on British withdrawal.
European Commission president Jean-Claude Juncker has been adamant that there can be no informal discussions with Britain until it invokes Article 50, triggering the start of the two-year countdown to the UK's final withdrawal.
But speaking to reporters at the Nato summit in Warsaw, Mr Hammond said the mood among individual member states was quite different.
"We absolutely understand that there are a lot of people who have become nervous and concerned, both British people living in the EU and Europeans living in the UK," he said.
"I hope we can get very soon to a reciprocal agreement which is fair to both the European Union nationals living in the UK and the British nationals living in the European Union.
"From our side we would be prepared to sit down with European Union counterparts immediately and talk about this particular issue on a reciprocal basis on the grounds that there is concern both by EU nationals in the UK and UK nationals in EU member states.
"But of course that conflicts with (the position of) the EU institutions, which is that there are to be no negotiations, discussions of any kind until after the Article 50 notice is served."
Mr Hammond said that despite the strictures from Brussels, informal discussions were already taking place with other member states about the possible terms of Britain's withdrawal.
"It is probably not an exaggeration to say that there is almost no other subject on the table when I get together with my colleagues," he said.
"We are in a Nato meeting but most of the discussions have not been about Nato issues, they have been about the outcome of the referendum and the consequences of that.
"Whatever noises might be coming from Brussels - which may be quite strident noises - that is not the mood in their national capitals."
Mr Hammond and Home Secretary Theresa May - the frontrunner in the Tory leadership race - have been criticised for using EU nationals in the UK as "bargaining chips" by refusing to guarantee their status.
However, he insisted that the Government had to be able to protect the position of British expats in the EU.
"Of course we could give a unilateral guarantee but I think that would be a dereliction of our duty to the 1.2 million British nationals living in the European Union," Mr Hammond said.