Both Tory eurosceptics and Labour want to keep the rebate, which has knocked billions of pounds off the UK's EU bills for more than 25 years. They - and Mr Cameron - insist in the face of commission calls for it to be ended that it remains appropriate as UK payments to the EU kitty are disproportionately high.
The IPPR argues, however, that offering it up as a bargaining chip "might be the most effective way" to persuade France - which would be the biggest loser from such a deal - and other member states to back significant reforms of the Common Agricultural Policy (CAP) and structural funds to pay for the cutbacks.
Reducing the overall budget by a quarter from £120 billion to £89 billion would save the UK £1.2 billion from the present contribution, it suggested, offsetting the loss of the rebate.
Associate director Will Straw said: "Britain should attempt a 'grand bargain' with Europe, offering to give up the rebate, but only in return for a smaller overall budget, meaningful reform of the CAP, and greater measures to enhance growth.
"To ensure that giving up the rebate is palatable to the British public it should be contingent on a reduction in the overall size of the budget so that Britain's contribution to the EU becomes smaller than it is today."