The high-ranking diplomats were speaking to Sky News under the Chatham House rule, which allows their comments to be reported, but not directly attributed.

One ambassador said: "[He] told us he was personally in favour of it, but he said that Britain had been more affected by free movement of people than other EU member states."

Another said that Johnson was even more forthcoming, saying:

"He did say he was personally in favour of free movement, as it corresponds to his own beliefs. But he said it wasn't government policy."

Corroborating the remarks, an ambassador for a third country said that he was "shocked" by the Government's shambolic diplomacy.

He said: "Boris Johnson has been openly telling us that he is personally in favour of free movement."

In a separate conversation yet another ambassador, speaking on condition of anonymity, said: "Yes, he told us at an ambassadors' luncheon."

Responding in Rome today, Johnson rejected the allegations:

"What I said, very clear, to that group of ambassadors – I think it was at a breakfast – was that immigration had been a good thing for the UK in many respects, but it had got out of control and that we needed to take back control. And I think you will find the record reflects that."

A spokesman for him had earlier commented: "Boris said what he has said many times before – he is pro-immigration but wants to take back control to limit numbers.

"He did not say he supported freedom of movement and challenges anyone to show proof that he ever said that."

The remarks he is accused of are incendiary as they seem to suggest the UK's top diplomat – and leading Leave campaigner – is taking one position in private and a directly contradictory stance in public.

Jonathan Lis, deputy director of the pro-single market think tank British Influence said:

"We are interested to learn that Boris Johnson supports free movement of people and is prepared to tell his negotiating partners as much – even though this appears to go against his public statements as Foreign Secretary, as well as the Government's self-declared red line.

"Of course, continued membership of the EEA would allow for single market access with some discretion over free movement – or if the Government agrees with the Foreign Secretary, full free movement as now."

Two weeks ago the Foreign Secretary was quoted in the Czech newspaper HospodáÅ™ské noviny as saying it was "b******s" that freedom of movement was a fundamental principle of the European Union.

They also contrast to comments he made ahead of the EU referendum. In a letter to David Cameron in May, he wrote:

"We are particularly concerned about the impact of free movement in the future on public services. 

"Class sizes will rise and waiting lists will lengthen if we don't tackle free movement."

Liberal Democrat EU spokesman Nick Clegg accused him of "treating the voters like fools".

Johnson's former Vote Leave partner Michael Gove defended Johnson, tweeting:

"Briefing against @BorisJohnson from some renegade EU sources is counter/productive – he is pro managed migration – the only sensible course."

The European Parliament describes the freedom of movement and residence for persons in the EU as the "cornerstone of Union membership", which was established by the Treaty of Maastricht in 1992.

Under Theresa May, however, the UK government is on course to prioritise controlling immigration above continued membership of the single market, as she prepares to trigger Article 50 by the end of March.

A fifth ambassador said he had not heard Boris saying those words, but was withering in his criticism.

"Johnson has no credibility with the ambassadors – they don't care what he says," he said.

Additional reporting by IRN