European leaders have already proved happy to hold informal talks on Brexit despite “strident noises” from Brussels banning such discussions, Philip Hammond, the foreign secretary, has said.

The senior Conservative said his talks with other foreign ministers at a Nato summit in Brussels had been completely dominated by informal exchanges about Britain leaving the EU and its consequences.

Hammond said the talks were about “smelling the atmosphere”, especially around the willingness of countries to guarantee reciprocal rights for Brits abroad and EU citizens in the UK. It was about “reassuring and exploring the art of what is possible”, he added.

He made the remarks after the EU ordered that no negotiations with the UK should start until article 50, the formal notice to leave, is triggered. “I don’t think anyone is pretending that means bilaterally we won’t be discussing all of these issues with member states,” Hammond said.

“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. 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.”

He added: “Whatever noises might be coming from Brussels, which may be quite strident noises, that is not the mood in their national capitals. In the national capitals, there is an understanding of the political realities, that what is done cannot be undone and there is a genuine desire to explore the way of Britain and the EU working closely together even as Britain ceases to be a member.”

Hammond also reiterated that the UK wants to get a move on with agreeing the rights of EU and British citizens abroad. His position is in line with that of Theresa May, the home secretary and Conservative leadership candidate, who has said EU citizens cannot definitely be allowed to stay without similar guarantees for Britons in other parts of the EU. This is in contrast to her rival, Andrea Leadsom, who has confirmed she would ensure all EU citizens have leave to remain.

Hammond said: “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. 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.”

Hammond’s comments come after he said last week that the issue was likely to be “a big moving part” in the UK’s Brexit negotiation, and would be one of the most politically sensitive issues. The UK government has been under intense pressure from Conservative backbenchers and others to give a unilateral guarantee that the rights of EU migrants in the UK will not be damaged at the end of the Brexit talks.

Giving evidence to the foreign affairs select committee, Hammond again said he could not give such a commitment and blamed “Brussels bureaucrats” for declaring there could be no informal negotiations until the official notice to leave was given. In practice, a total ban on informal talks is unenforceable, but the UK will have to tread carefully not to overstep the commission’s attempt to block such talks.