A Tory donor has said he will stop funding the party if Theresa May takes the UK out of the single market.

Sir Andrew Cook said jobs and exports were at risk if Brexit meant membership of the single market was sacrificed in order to curb immigration.

Cook, who has given more than £1.2m to the Conservatives, said the country could “sleepwalk to disaster” if the prime minister decided to go down that route, the Times reported.

Cook, the chairman of William Cook, which produces components for applications including rail, energy and defence, highlighted how much his company relied on exports to mainland Europe and the supply of skilled labour from the continent.

Speaking from Sheffield, he told BBC Radio 4’s Today programme: “I’m trying to explain how critical the single market is to the real economy. Two miles away is one of my factories, with 200 people employed making engineering parts that go to France, Germany and Italy for pumps and so forth.

“Thirty-five miles up the road in Leeds I’ve another factory with 200 people making other stuff for the train manufacturers of Germany, Austria and so forth. The single market is essential to keep these people in employment.”

He added: “There are barriers to entry without the single market, there are tariffs. There is a desire by my competitors in mainland Europe to exclude me from the market. Were it not for the single market I would not be trading with these people.

“There is no domestic manufacturing industry of any major size in this country with which to trade. It is vital to these jobs and people that are trying to reduce the chronic and dangerous balance of payments deficit that this country suffers from.”

Cook, who was treasurer of the Conservative In campaign in the 2016 referendum, said the ideas of free movement and paying money to Brussels had not been properly considered by voters.

“I don’t think they were chucked out on the basis of sensible information. The fact of the matter is that the amount of money that we contribute to the European Union was always portrayed by the leavers as a gross sum without anything in return.”

Cook said he had a number of Polish machinists at his plant in Leeds, adding: “We are talking about EU citizens, with skills, coming here to fill jobs that British people are either unable to do or don’t want to do.”

Asked whether he thought his concerns would be listened to in Westminster, he said: “I think some people will take me into account, others will not. This is a very diverse country, there are different views depending on who you are, where you are and, if you are a politician, where your constituency is.”

He told the Times: “It seems to me the political tail is wagging the economic dog. There appears to be a willingness to consider the sacrifice of withdrawal from the single market, which I believe will be a catastrophe.”

May has said she wants firms to have the “maximum freedom to trade with and operate in the single market”, but her desire to secure curbs on immigration suggests that the UK will have to give up its full membership.

EU leaders have repeatedly stressed that free movement of its citizens is a condition of single market membership that will not be negotiated away.