An analysis by the economic forecasting consultancy Oxford Economics found that a £500m-a-year real-terms cut in charity incomes would cost between £1.2bn and £1.5bn in lost benefits to society. It would also lead to around 10,700 job losses at charities.

The new figures come as leading members of the charitable sector met the Treasury minister, David Gauke, and the Civil Society minister, Nick Hurd, to discuss the cap and its effects on large charities.

David Cameron had been due to meet representatives from volunteer organisations in London’s Natural History Museum following the Giving Summit, but the idea was ditched amid fears that it would be dominated by the row over the tax cap. Instead, meetings with ministers were held behind closed doors.

Treasury sources have suggested two possible government concessions in an attempt to heal the rift. One idea is that the cap could be lifted from 25 per cent to 50 per cent for donations to charity, and that donors could roll over unused reliefs from one year to the next. But charities say they will only settle for a complete exemption for the sector.

The research by Oxford Economics looked at the “multiplier” effects of donations to the charitable sector on the wider UK economy. It found that the loss of £500m in donations as a result of the tax change would equate to between £1.2bn and £1.5 bn in real costs.

John Low, chief executive of the Charities Aid Foundation, said the cost of the move to charities was disproportionate to the extra revenue the Treasury would get.

“The reality is that this tax change will yield relatively small amounts for the Treasury but threaten large cuts in charities, which are already hard pressed in the current economic climate,” he said.