And he pledged the government would support charities helping those caught up in the Boxing Day deluge by matching every pound of the first £2m raised.

The cash takes investment in recovery from Storm Eva and Storm Desmond to nearly £200m.

The package is now set to be extended with grants to reimburse fire and rescue authorities that have incurred excessive costs protecting flooded communities. 

Prime Minister David Cameron said:

I have seen at first-hand the devastation caused by flooding. And that’s why this work to repair and improve flood defences is so vital.

We are already spending £280m over the next 6 years to protect thousands of houses from flooding in Yorkshire as part of our £2.3bn investment to protect 300,000 houses across the country.

But now more than £40m will be spent to fix those defences overwhelmed by the record rainfall we’ve seen in recent weeks and to make them more resilient to further bad weather.

The Prime Minister announced £10m of the new funding package would be reserved to improve the Foss Barrier protecting York, which was overwhelmed at the height of Storm Eva.

The other £30m will be spent repairing defences on the Wharfe, Calder, Aire, Ouse and Derwent. It will include repairs to pumping and barriers and clearing blockages in rivers.

Further detailed work will be conducted along all rivers affected by Storm Eva – and it is very likely the overall bill will top £40m once the full damage is identified.

The announcement of matched funding for charities follows a similar pledge made to community foundations in Cumbria and Lancashire in the aftermath of Storm Desmond.

Applications for areas affected by Storm Eva can be made by any registered charities that are currently running a fundraising appeal for flood relief to benefit affected areas.

The flooding response in Yorkshire will be overseen by Transport Minister Robert Goodwill, who has been appointed by the Prime Minister as Flooding Envoy to the county.

Robert Goodwill’s role will complement the work of Flooding Minister Rory Stewart as envoy for Cumbria, Lancashire and Northumberland.

As a Ministerial Flood Recovery Envoy for Yorkshire, Robert Goodwill has been tasked with:

• understanding the impact of flooding in affected areas, especially weaknesses exposed
• tracking progress towards recovery and reporting directly to the Prime Minister
• assessing the effectiveness of multi-agency joint working in affected areas (for both response and recovery); and
• identifying lessons learned

Robert Goodwill and Rory Stewart will report into the Flood Recovery Committee chaired by the Secretary of State for Communities and Local Government, Greg Clark.

Meanwhile, the government’s political opponents have heaped criticism on ministers’ responses to flooding.

In the wake of Storm Eva, Green Party leader Natalie Bennett said the government’s had been a “Wholly inadequate response to the massive disruption to communities, lives and economies, and a demonstration of the way this government has failed to respond to the reality and threats of a world now already living with one degree of warming above pre-industrial levels.”

Bennett said, “It has been clear since its election that this government hasn’t grasped the reality of the climate change we’re already experiencing – which the experts tell us will result in more extreme weather, and extremes happening more often.

“We urgently need to not just consider flood defences, but land use across catchments, plus the protection of urban areas through sustainable drainage and similar management schemes, while ending the construction of new housing estates in vulnerable areas. And we urgently need the government to adopt the policies that will ensure we play our part in restricting climate change to a total of 1.5 degrees warming.”

After the second wave of December flooding struck northern counties on Boxing Day, Labour’s shadow environment secretary Kerry McCarthy said “It is increasingly clear that so-called ‘unprecedented’ weather events are here to stay. The Government must drop its complacency over the need for climate change adaptation [and] look urgently at what else can be done to reduce flood risk in future.”

In response to the Prime Minister’s funding announcement, she said the government had taken a “Short-term, sticking-plaster approach” to repeated flooding.

Lib Dem leader Tim Farron, whose Westmorland constituency was hit by flooding, also compared the funds unveiled by the prime minister to estimates showing the cost of flooding in Cumbria to be in excess of £500m.