At the weekend, the Prime Minister saw his Tory rival Boris Johnson and five full Cabinet ministers come out in support of a British exit from the EU, ahead of the in/out referendum on June 23.
More than 100 Tory MPs are now backing Brexit, after snubbing their party leader’s EU renegotiation deal.
And today Mr Cameron saw lesser support from big businesses for his bid to keep the UK tied to Brussels than it is believed Downing Street had initially hoped for.
The chairmen and chief executives of 36 of the FTSE 100 companies signed a letter calling for Britain to remain in the EU.
But, at the beginning of the week, it had been suggested up to 50 to 80 companies would sign the letter.
Tesco, Sainsbury”s and Barclays were notably absent from the list of top British companies signed up to the letter, although BT, Asda, Marks & Spencer, Kingfisher, Vodafone and the chief executives of Heathrow and Gatwick airports signed up to the pro-EU message.
Quizzed today on whether he felt his opponents in the Leave campaign had now seized momentum in the EU referendum debate, the Prime Minister admitted it was going to be a “very hard-fought contest”.
Speaking to O2 staff members at a question-and-answer session at the mobile phone company’s offices in Slough, Berkshire, he said: “They are very strong arguments on both sides, there”ll be very strong figures on both sides.
“But when it comes to business and industry the overwhelming view I am getting is that British business, particularly those that trade a lot with Europe, really want us to stay in the EU.
“For 36 FTSE 100 companies to come out and say this so clearly as they have today, I think that is a very positive, very clear decision by them and a very clear message that they”re saying: ‘We”ll be better off if we stay in’.”
Mr Cameron suggested companies often find it “quite difficult” to make political statements, after being asked why nearly two-thirds of FTSE 100 companies weren’t represented on the letter.
The Prime Minister said: “For companies these days to make a statement like that, they find that sometimes quite difficult, they have to go through corporate governance proceedings or board meetings to make those decisions.
“Many business don”t want to get involved in any political issue.
“But I would say to them, this is not like a general election, it”s not about backing one team or another team.
“This is a decision that we are going to have to live with in Britain for decades to come.
“If you have a strong view, you should make it clear.”
Mr Cameron argued the letter was “not business leaders telling people how to vote” but “simply people running some of the largest businesses in our country – that employ over a million people between them – saying this has real consequences for our country.”
The Prime Minister urged other groups such as trade unions, charities and universities to “speak out” during the referendum debate, adding: “I don”t think anyone should hold back, I”m certainly not going to hold back.”
Mr Cameron also claimed pro-Brexit groups would be “over the moon” to receive similar business support for their campaign.
But Northern Ireland Secretary Theresa Villiers, one of five full Cabinet ministers backing Brexit, later cited a “long list of businesses” that have said they will continue to invest in Britain even if voters decide to leave the EU.
She told BBC Radio 4″s World at One: “Of course people will want to listen to the views of business leaders, but I think it”s clear that the business community has a divided opinion on this.
“I think if you look through the 198 who signed the letter, I”m sure you will find names which 10 or 15 years ago were saying the UK had to join the euro and it would be a disaster if we didn”t. They were wrong then and they”re wrong now.”
Ms Villiers added: “There”s also a long list of businesses – like Vauxhall, Airbus, GE, Renault – all of whom have said they will continue to work and invest in the UK even if we leave.
“The reality is the EU sells more to us than we do to them, so if we left it would be in their interests to have a trade deal with us. So we”d carry on doing business with the rest of the EU even if we left.”
Brexit groups also dismissed the show of support from British businesses for continuing the UK’s membership of the EU.
Richard Tice, co-founder of the Leave.EU campaign, said: “We remember well how many large businesses and EU funded groups like the CBI said we should join the euro. How wrong they were.”
He added: “The truth is that despite the bullying of a prime minister who has no real business experience, it is other normal commercial factors which will determine the continued success of British businesses to invest and grow.
“Brexit will reduce unnecessary regulatory burdens and cost on business, which can be used to invest in more jobs, not less.”
Vote Leave chief executive Matthew Elliott said: “Panic seems to be spreading in Number 10 as support for David Cameron”s deal plummets.
“The EU treaties will only change by 1 per cent if it ever comes into force – there is very little reform on the table.
“The only way to take back control of our economy to help British businesses to flourish is to Vote Leave.”