A ministerial colleague of Chris Grayling has insisted the cabinet still supports the beleaguered transport secretary, amid pressure on him to step down over the cancellation of a Brexit-related ferry contract awarded to a company with no ships.

The backing from James Brokenshire, the communities secretary, came as the Irish government dismissed the idea that it had influenced the demise of the £13.8m deal with the startup firm Seaborne Freight.

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After the news emerged, several MPs said Theresa May should sack Grayling. Bob Kerslake, the former head of the civil service, said the arrangement would “just confirm the view of many that this country is in a mess”.

Asked if he had confidence in Grayling, Brokenshire told the BBC’s Andrew Marr Show that the transport secretary had “done a huge amount of work to prepare for our departure from the EU”.

Pressed on whether this meant he had faith in Grayling, Brokenshire said: “Yes, I think Chris has done a really tough job, really, really positively to ensure that we are well prepared. I strongly endorse all the work Chris has been doing.”

The awarding of the contract to Seaborne to charter and operate freight ferries from Ramsgate to the Belgian port of Ostend if the UK leaves the EU without a deal was announced in December. But the news was soon dominated by the fact that the firm had no ships and had seemingly borrowed the terms and conditions on its website from a food delivery firm.

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The transport department said the contract had been ended after Seaborne Freight’s financial backer, Arklow Shipping, an Irish firm, decided to “step back from the deal”.

The Brexit-backing Conservative MP Jacob Rees-Mogg questioned at the weekend if Arklow’s move had taken place at the behest of the Irish government. But Helen McEntee, Ireland’s European affairs minister, tweeted: “The first time the Dept of Transport heard about it was on the radio this morning. Absolutely no truth to it.”

When the news emerged, the Conservative MP and former business minister Anna Soubry said Grayling “should be quietly considering his position”.

She said: “Chris Grayling holds a critical position in government, trying to mitigate what would be a very serious crisis for the country if we leave the European Union without a deal. He has no grip on the very serious nature of his job. The prime minister should also be considering whether there is not someone else who could do the job better.”