David Cameron is under renewed pressure to spell out ambitious EU renegotiation demands as he prepares for a crunch summit this week.
The Prime Minister is expected to formally notify counterparts that he is seeking a new deal for Britain at the European Council meeting in Brussels on Thursday.
But in public he has so far kept his agenda general, citing goals such as a four-year ban on EU migrants claiming in-work benefits, greater protections for non-eurozone countries, an opt-out from the "ever-closer union" principle, and more power for national parliaments.
Allies are said to have been trying to reassure restive Tory MPs that this is merely the "tip of the iceberg", suggesting that Mr Cameron could also seek an opt-out from social chapter workplace regulations and a cut in the UK's EU budget contributions.
There is also speculation that he could attempt to "rebrand" the relationship with the EU by having Britain described as an "executive" or "associate" member.
However, the Business for Britain pressure group have laid down the gauntlet to the premier in a report that argues he needs to secure far more radical concessions.
The analysis, written by senior business figures including John Moynihan and John Mills, says treaty change is "essential", the arrangement must be more like a free trade area than a political union, and powers must be reclaimed.
Mr Moynihan, former executive chairman at PA Consulting, said: "David Cameron has a mandate to seek wide ranging reforms of the EU to ensure Britain achieves the looser, economic-based trading relationship it voted for 40 years ago.
"Either we change, or if we can't secure the change that we need, leaving an unreformed EU will be the right course to plot for Britain's future prosperity in an increasingly globalised economy."
Speaking on the BBC's Sunday Politics, former defence secretary Liam Fox said Mr Cameron had to give more information about his negotiating position.
"Certainly as we go into the autumn season, into our party conference I think it will be necessary to reveal a little bit more of what we're negotiating. And if there's going to be, as has been widely speculated, a referendum date in October next year then we will have to find out some of those details much sooner," he said.
But leading Tory pro-European Ken Clarke said opponents of the EU were trying to get Mr Cameron to make demands that could not be met.
"They want us to leave, they don't want reform," he told BBC Radio 5 Live. "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."
The issue of renegotiating British membership is not on the formal agenda for the Brussels summit - although Mr Cameron has spent the past few weeks circling the continent to lay the groundwork with the other 27 leaders.
The Prime Minister's moment at the gathering in Brussels could yet be overshadowed by the crisis over Greece, which is engaged in desperate last-minute talks with eurozone members to extend its bailout funding.
Failure to strike a deal could see the country default on its debts and exit the currency area - and possibly the EU - causing major economic shockwaves.