David Cameron could attempt to "rebrand" Britain's membership of the EU

Mr Cameron is due to continue his push for a new relationship with Europe at a key summit in Brussels on Thursday - although there are concerns his agenda will be overshadowed by the growing Greek crisis.

The Tory leader has been coming under increasing pressure from his backbenchers to flesh out his demands, which up to now have publicly been limited to four areas: curbing migrant benefits; an opt-out from the principle of "ever closer union"; more power for national parliaments; and protections for non-eurozone states.

Allies have been trying to placate restive MPs by suggesting that they are only seeing the "tip of the iceberg".

They have apparently mooted restoring Britain's opt-out from the Social Chapter workplace regulations, and cutting contributions to the EU budget.

In order to emphasise the changes, the new deal could involve the UK being given a special membership status, the Sunday Times said.

However, the idea was dismissed by leading Eurosceptic Bernard Jenkin. "The offer of a two-speed or two-tier EU is no concession at all," he said. "We would continue to be taken for a ride on the road to second-class membership in an EU that as a whole is proceeding with continued political integration."

Conservative former chancellor Ken Clarke, a prominent pro-European, suggested the concept was "meaningless".

"What on earth does it mean unless you just want to deliberately reduce your role in the way in which the European Union is run despite the fact we're heavily dependent on the success of the European Union as a country," he told BBC Radio 5 Live's Pienaar's Politics.

"I think our membership of the European Union is the way of looking after our interests in the modern world. The question in the referendum is not going to be about the details of negotiations or the title of our membership, it's about whether or not Britain can best look after our own interests in today's world as a leading member of the EU, and whether the right base for our economy in a globalised economy is with full access to this big market with full influence in what the rules of the market are."

Mr Clarke said Eurosceptics were trying to force Mr Cameron into making "demands which they know are quite incompatible with the European Union".

"They want us to leave, they don't want reform," he added. "They are all right-wing nationalists, the ones that call themselves Eurosceptics, it's the Murdoch press that's so wildly excited about all that kind of thing."

Conservative former cabinet minister Liam Fox said he would be unhappy if his party used its funds to campaign to stay in the EU.

He told BBC 1's Sunday Politics: "I think the Conservative Party itself is likely to be split in two ways.

"I think the parliamentarians inside the Conservative Party will have a split in one direction. I'd have thought the party activists and membership might be very split on another.

"And I would have thought it would be those activists and members who would object to not just the party's money, which I imagine isn't hugely enormous after the election, but the party's machinery - our email addresses and the information we have on voters - that should not be used in my view to campaign in a party political way in a campaign which will not be party political."

Asked if the PM would risk splitting the Tory party if he insisted on collective responsibility from Cabinet ministers during the referendum campaign, Mr Fox said: "If the Prime Minister was to insist on Cabinet collective responsibility during the referendum I'm sure he could get it - I'm just not sure he would have the same Cabinet."

Pressed if that meant some would resign, he said: "I'm pretty sure some would.

"For a lot of people this is the only opportunity they have had in their lifetime - including myself - if you're under 58 in this country you've never had a chance to have a say on our constitutional relationship with Europe, and it's too important an issue to allow it to be subjected to any other considerations."

Ukip MEP Steven Woolfe said his party's leader Nigel Farage should go head to head with Mr Cameron in a TV debate during the referendum campaign.

He said Mr Farage "destroyed" the then Liberal Democrat leader Nick Clegg ahead of the 2014 European elections.

Speaking on BBC1's Sunday Politics, Mr Woolfe said: "One thing will be certain - when Nigel Farage debates David Cameron - who doesn't want to do it, he tried to avoid it during the general election - he will be defeated on every single point, because David Cameron doesn't believe in ensuring this country leaves the European Union, he wants to seek very feeble changes which won't have a major impact."

Meanwhile, supporters of Brexit are gearing up for the coming campaign.

A group of tycoons including insurance mogul Arron Banks are putting together an apolitical group to push the case for leaving, with a former army general said to be in talks to act as its leader.

The Sunday Telegraph reported that the body has been provisionally titled No Thanks - We're Going Global, and offices are being set up in London this month.

An agency has been hired to prepare a major PR and advertising blitz to coincide with its launch on September 10. So far, £7 million of a £20 million fundraising target is said to have been pledged by backers including Mr Banks.

Mr Banks, who donated £1m to Ukip before the general election, said the campaign would deliberately have nothing to do with Eurosceptic Tory or Ukip politicians.

He told the newspaper: "We represent a group of entrepreneurs, businessmen who are very different from the same people who go around the Westminster bubble.

"We see the need for a public campaign, rather than all the Eurosceptics just talking to each other.

"This is too important for politicians to be taken the lead, it has got to be business, and the wider public.

"We have been talking to sports stars, leaders in fields of medicine and science, and military figures.

"Nigel (Farage) is a great communicator but I don't believe Ukip is the right vehicle to take this forward. It is not a political campaign.

"This is too important to leave to politicians. They can endorse it and support it but they will not be involved in the campaign.

"Nigel is not the right person to lead the campaign. He does not reach out to everybody."