POLL: Should UK security services be used as a bargaining chip during EU talks?

Sir Michael said he was proud of the link and insisted the UK would go on "playing our part" in the security of the continent, but stressed some elements of that co-operation would require a new deal.

He claimed it was not a "bargaining process" but all sides would be "worse off" if there was not a deal.

Leaked minutes of a Cabinet committee meeting revealed the extensive discussions about how the UK's security and defence expertise could be used to help secure a deal with Brussels.

The Sunday Telegraph reported ministers identified the UK's "very strong hand" on defence as a key advantage in the talks.

Downing Street has insisted the reference in Theresa May's Article 50 notification letter to security, warning that co-operation would be "weakened" if there was not a deal, was not a threat but a simple statement of facts.

Sir Michael told BBC One's Andrew Marr Show: "It's very important to link trade and security because what we are now looking for is a deep and special partnership that covers both economic and security co-operation. Those two things go together."

He was "absolutely" proud of that link, adding: "It's very important that we go on committing to the security of the continent."

Asked if failure to secure a deal would make the EU less secure, he said: "We would all be worse-off it there wasn't a deal. We are expecting to have a deal.

"Obviously, we co-operate with Europe on security, not just through Nato - we co-operate through work our police forces do, our security agencies do, through our judicial systems.

"Some of that is inside the European treaties, some of it is outside.

"But obviously the bits that are inside the European treaties we need to make sure that co-operation continues, because Europe faces threats - not just from Russian aggression but, as we have seen in recent weeks, from terrorism as well."

Asked about the Sunday Telegraph report, he said: "I'm not going to get into what happened at what meeting, but it is a fact that we have the biggest defence budget in Europe, we are a leading player inside Nato."

A source quoted in the newspaper said: "I think the absolute view around the table was we are in a very strong position and the Europeans know it.

"We go into these negotiations with security and defence being a big thing in our corner."

In her letter to Mr Tusk, Mrs May had warned: "Europe's security is more fragile today than at any time since the end of the Cold War.

"Weakening our co-operation for the prosperity and protection of our citizens would be a costly mistake."

Sir Michael refused to be drawn on the details of any "implementation" agreements which could cover trade and the economy after Brexit during the process of shifting to a new deal.

Pressed on whether free movement could still be happening and the UK could still be subject to the European Court of Justice at the time of the next election, he said: "No, we have made it clear that we are leaving the European Union, we are leaving the single market, we are leaving the customs union and we will no longer be under the ambit of the European Court of Justice.

"It is also clear that we have to avoid a cliff edge.

"We need to give business and the various sectors of our economy the certainty that they need that there won't suddenly be a huge difference between the day after we leave and the day before."

Shadow foreign secretary Emily Thornberry said it was important that any deal should protect national security, but co-operation should not be a bargaining chip.

"Not only are they threatening the European Union, they are threatening us," she told BBC Radio 5 Live's Pienaar's Politics.

"Amber Rudd has said that if we don't get a deal she will stop sharing information with Europol. Are they seriously saying that if they know about a terrorist attack in Paris they won't tell Europol?"

She added: "Either they mean it, or they don't mean it. They can't just keep saying things."