Less than a third of a £110m fund agreed by the European Commission to help worst-hit areas will actually reach the UK.

A staggering £79m – which would have helped families and businesses in Sheffield, Rotherham, Barnsley and Doncaster hit by the disaster – will be swallowed up by a complex funding mechanism which sees the UK penalised for paying less money into EU coffers than others.

The cut in EU cash was slammed by one Sheffield woman, whose home was flooded twice last June. Barbara Parkin, of Falding Street, Chapeltown, said: "It beggars belief. Over the years we've certainly paid in enough to Europe. And we're always giving money to other countries when they need it.

"When we need the money, why can't we have it? We've never asked for anything like it before."

The controversy stems from an application last year by the government to the EU's Solidarity Fund – a cash pot set up to help countries recover from major disasters such as floods and earthquakes.

In October flood recovery minister and South Yorkshire MP John Healey announced that Danuta H'bner, the European Commissioner for regional policy, had agreed to recommend to other EU chiefs that the UK be handed around 160 million euros – £125m – from the fund.

The EU Commission later approved a £110m payment to help offset the estimated £3.2 billion of damage caused by the floods last June and July, which hit thousands of private homes as well as businesses and road networks.

However, the Government has now made clear that under the so-called UK abatement mechanism, the total Brussels disaster relief will shrink to £31m.

The mechanism, which dates back to 1984, makes adjustments to EU payouts based on the amount the UK pays into the overall European budget.

Because the UK pays in less proportionately than some other countries, it loses two-thirds of any unexpected payments made from Brussels – including payouts following natural disasters.

Wentworth MP John Healey admitted he was "disappointed" the government had failed to secure an exemption from the strict funding rules.

He said: "We have never had a successful application to this fund before. We have asked whether the payments could be an acceptable exemption to the abatement but that arrangement allows no exemptions at all."

He stressed the £31m which was granted will be made available to the councils, police forces and fire brigades who bore the brunt of the clear-up and recovery work last year.