Theresa May on Thursday embarked on a Brexit charm offensive in Brussels, amid warnings from a senior diplomat that a final exit deal could take a decade to complete.

Mrs May will tell an EU summit that Britain will play a full role in tackling migrant flows from north Africa to Europe, even after Brexit.

She will also reassure fellow leaders from Latvia and Lithuania that Britain will fully support Nato efforts to deter Russian expansionism in the region.

Separately Mrs May will tell Martin Schulz, European Parliament president, that she supports his bid to win a bigger role for MEPs in Brexit negotiations.

But Mrs May will leave the one-day summit early to allow the remaining EU 27 countries to discuss over dinner how they intend to approach Brexit.

There is great scepticism in Brussels about claims by Brexit minister David Davis that exit talks and a new trade deal can be agreed within two years.

The BBC reported on Thursday that Sir Ivan Rogers, Britain’s ambassador to the EU, had privately told the government that a post-Brexit UK-EU trade deal could take a decade to finalise.

That advice is consistent with the message from Whitehall in the run-up to the June referendum. A study published in 2015 suggested that complete detachment from the bloc could take 10 years.

Sir Ivan told ministers that the view in other European capitals was that a deal may not be finalised until the “early to mid-2020s”. Even then an agreement could be rejected by other national parliaments within the EU during the ratification process, he added.

The government’s position is that a deal can be made during the two-year exit process that follows the triggering of Article 50.

Sir Ivan also told ministers that European leaders expected a free-trade deal, rather than continued membership of the single market. That is consistent with the consensus in Westminster.

Downing Street said on Thursday that the diplomat was passing on other EU members’ views rather than his own or the government’s.

Nick Clegg, former Lib Dem deputy prime minister, said: “I worked with Ivan Rogers in Brussels on trade deals 20 years ago. He knows what he is talking about — the government should listen.”

But Eurosceptics including Dominic Raab, a former minister, said Sir Ivan was being too “pessimistic”.

Mr Raab told the BBC that it was reasonable to set out a “worst case scenario” of five to 10 years to agree a trade deal. What was more important, he insisted, was whether Britain negotiated barrier-free trade with the EU in the meantime.

Sir Ivan “was the diplomat who persuaded David Cameron to dilute his ambitions for the renegotiation, which was one reason why the referendum was lost, so he’s been scarred by his own pessimistic advice in the past”, he said.