Theresa May used her interview on the BBC’s Andrew Marr programme this morning to defend her “ambitious” and “credible” plan for Brexit.

The interview, recorded on Friday afternoon and broadcast today, did not add too much to her big speech, but it did highlight she does not want the City of London to have EU “passporting” rights.

It was Simon Coveney, the Irish deputy prime minister, who actually made the most interesting intervention. Speaking to Marr before the PM, he said the EU could reject the UK’s Northern Ireland border plan. 

Also this morning, David Lidington dismissed Sir John Major’s demand that MPs be given a free vote on the eventual deal. John McDonnell said Tom Watson should “consider seriously” his financial arrangement with Max Mosley. Pro-EU Tory rebels appear to be softening their stance but Nicky Morgan warned May they were watching for any “drifting backwards towards some kind of ideologically driven hard Brexit”. Donald Trump was asked if he could please not start a trade war. And “steady on”, Nicola Sturgeon was asked if she would back a statue of Margaret Thatcher.

May told Marr that if the UK was to accept “passporting” after Brexit then “we would just be a rule taker, we would have to abide by the rules that were being set elsewhere”.

The passporting system currently allows British financial firms to sell their services right across the EU. May said instead she wanted a the new trade deal to allow the City access to the single market. “Given the importance of financial stability, of ensuring the City of London, we can’t just take the same rules without any say in them,” she said.

Everyone was “welcoming” May’s speech this morning, but there are already warning signs.

Simon Coveney, the Irish deputy prime minister, told Marr he was “not sure that the European Union will be able to support” the UK’s plan to avoid a hard border between Northern Ireland and the Republic of Ireland.

“While of course we will explore and look at all of the proposed British solutions, they are essentially a starting point in negotiations as opposed to an end point,” he said.

“She hasn’t really gone into any more detail than we’ve already heard in terms of how she is going to solve the problem of maintaining a largely invisible border on the island of Ireland.”

David Lidington, who had clearly read his script, appeared on both ITV’s Peston on Sunday and the BBC’s Sunday Politics. He managed to crowbar in the idea that May’s Brexit plan was both “ambitious” and “credible” on both shows.

Speaking to Peston, the Cabinet Office minister, who campaigned for Remain, hit back at Sir John Major’s call for May to grant free vote in parliament on the deal. “I think she is entitled to expect her government and her party to support her in that,” he said. “I would hope that the deal that she brings back would also attract a lot of cross party support as well.”

Lidington added it would be “dangerous” for parliament to look like it was trying to overturn the referendum result. 

Pro-EU Tory MPs, who have been threatening to vote against the government, appeared to be softening their stance somewhat today.

Sarah Wolllaston said she wanted to give May “breathing space” after her speech and said the amendments to the Trade Bill would “probably be kicked down the road a bit”.

Nick Morgan, another leading rebel, claimed the amendments,, which would keep the UK in a customs union with the EU, were all about the Northern Ireland border issue.

But she added: “We welcome the speech but we will continue to watch out for any drifting backwards towards some kind of ideologically driven hard Brexit.”

Over on Sky News’ Sunday with Niall Paterson, John McDonnell warned Tom Watson to think again about his relationship with press regulation campaigner Max Mosley.

Last week a leaflet apparently published by Mosley in 1961 claimed “coloured immigration threatens your children’s health”.

Mosley has donated £500,000 to Watson. Labour’s deputy leader has said he accepted the money on the understanding Mosley’s “views had changed from years ago”.

But McDonnell this morning said it appeared Mosley had not changed his opinion. “If those are the same views now well Tom will really need to consider seriously exactly that relationship with Max Mosley and the finances as well,” he said. “Because if he is reiterating these views from the past he really hasn’t changed.”

May’s interview was conducted on Friday in Downing Street. The pre-record meant Marr was not able to ask the prime minister about Donald Trump’s threat to launch a trade war with the EU and slap tariffs on car imports.

David Lidington, the cabinet office minister, told the BBC’s Sunday Politics that “trade wars don’t do anybody any good”. He told President Trump that “the US is not taking an advisable course”.