Latest EU referendum polls: Remain on 45% and Leave on 43% as small businesses warned of impact

The Cabinet minister said it was a "dangerous" misconception to believe that smaller firms would be unaffected by Brexit.

His comments came as the rival camps clashed over spending pledges, with senior Vote Leave figures claiming energy bills could be cut after Brexit, but Remain accusing them of "fantasy economics".

Speaking in Birmingham, Mr Javid said small firms were the "backbone of our economy" and the livelihoods of millions of workers could be put at risk if the country breaks from Brussels on June 23.

He cited analysis by the Department for Business, Innovation and Skills (BIS) estimating that 8% export to the EU and a further 15% are in the supply chains of other businesses that export to the EU.

Britain Stronger In Europe said that amounted to around 1.2 million firms if you include the smallest businesses, including non-employers, which do not have to register to pay VAT.

BIS qualifies its estimate of what proportion are directly or indirectly involved in EU exports as "indicative estimates" as it uses data whose definitions "do not entirely align".

Mr Javid said: "Make no mistake: if we vote to leave the EU, small businesses will be hit hard.

"You may have heard the myth that only massive multinationals want us to stay in the EU; that small businesses want out; that hardly any small firm exports to the EU, so leaving it won't be such a big deal.

"That's just plain wrong. It's a misconception that could have dangerous consequences for millions of people who rely on small businesses for their jobs and for their livelihoods."

Mr Javid added: "Without the single market, those tariffs, those custom checks, the bureaucracy of the past - they would all make a screeching return.

"Big businesses might be able to cope with that - they might cope with many of the additional costs. You could argue they have the capital, they have the compliance departments, they have they lawyers, that they would negotiate the years of uncertainty that would be created.

"But small businesses just don't have that."

Business TV stars including Apprentice boss Lord Sugar and seven past and present members of the Dragons' Den panel added their voices to the Remain camp.

In a video message, Lord Sugar warned that Brexit would be a "massive mistake" and was a "daft idea".

"This is a gamble that we cannot afford to take," the Government's Enterprise Tsar said.

"I have been in business for many years and I have seen plenty of daft ideas and duff proposals in my time and Britain leaving the European Union is one of them."

The Dragons' Den stars said they would not back the "reckless risk" of leaving the EU as the Remain camp claimed 1.2 million smaller firms would be directly affected.

The statement from the Dragons was signed by James Caan, Hilary Devey, Kelly Hoppen, Touker Suleyman, Sarah Willingham and Simon Woodroffe, along with Piers Linney, who appeared at the event with Mr Javid.

John Longworth, former director-general of the British Chambers of Commerce who now chairs the Vote Leave Business Council, said: "These Government figures are extremely questionable.

"The reality is that only 6% of British firms export to the EU, but 100% are caught up in red tape and costs from Brussels. If we Vote Leave and take back control of our economy, our businesses will thrive."

Britain Stronger In Europe claimed that Brexit-backers had made almost £112 billion in spending commitments using the money that would be saved by quitting the EU.

Chancellor George Osborne warned the economic damage of leaving the EU could mean a rise in taxes as he challenged the case put by Tory colleagues Boris Johnson and Michael Gove and Labour Brexit-backer Gisela Stuart that VAT on energy bills could be cut if the UK votes to break from Brussels on June 23.

In a joint article in The Sun, Mr Johnson, Mr Gove and Ms Stuart promised that "fuel bills will be lower for everyone" because the UK could scrap the tax imposed by a Conservative government in 1993.

In a pitch aimed at working-class voters, they said: "As long as we are in the EU, we are not allowed to cut this tax. When we vote Leave, we will be able to scrap this unfair and damaging tax."

Mr Osborne said: "More fantasy economics from Vote Leave: leaving EU would lead to smaller economy, a hole in public finances + higher taxes - like higher VAT."

The Remain camp estimated the cost of various ideas suggested by Brexit campaigners at nearly £112 billion, but Vote Leave chief executive Matthew Elliott dismissed the claims, saying: "BSE (Britain Stronger In Europe) are simply making up numbers and have invented pledges that don't exist.

"If we Vote Leave, we can spend the £50 million we hand to the EU every day on our priorities, like using a small proportion of it to cut energy bills and ease the pressure on family budgets.

"The Remain campaign should admit that if we vote In, then Brussels will be in charge of VAT levels and will continue taxing low-income families."