Environment Secretary Owen Paterson has been confronted by angry residents in an area badly hit by flooding.
Farmers and MPs in the Somerset Levels have accused the government and the Environment Agency of failing to take action by dredging the rivers.
The agency has said increased dredging would not have prevented recent flooding.
Mr Paterson promised an action plan would be drawn up to provide a long-term solution.
The Environment Agency currently has 14 flood warnings in place, 10 of which are in south-west England, where more rain is forecast over the coming days.
An agency spokesman said: "We're doing everything we can to pump water off the Somerset Levels as quickly as river and tide levels allow.
"We have brought in extra manpower and pumping equipment from around the country and have 65 pumps working around the clock. This is the single largest pumping operation ever undertaken in Somerset."
But he added: "Dredging is often not the best long term or economic solution and increased dredging of rivers on the Somerset Levels would not have prevented the recent widespread flooding."
As Mr Paterson visited the Somerset Levels - a wetland, which is one of the lowest and flattest areas of the country - local farmer Becky Riley said more should have been done sooner.
She asked: "Why was this not done last year, when this happened last year? Why have we just had the pumps put in now, why?"
Mr Paterson said he wanted to see a "concrete plan" from "all the interested parties" - including the local authorities, the Environment Agency, Department for Environment, Food and Rural Affairs, the Department for Transport, the internal drainage boards and the Department for Communities and Local Government - to provide a long-term solution, submitted to him within the next six weeks.
The minister added the plan would "almost certainly" involve clearing the Parrett and Tone rivers, acknowledging that national guidelines on dredging did not apply in the area as so much of it is below sea level.
Mr Paterson said: "I've come down here to see what can be done. It appears from what everyone's telling me that we do need to dredge these two rivers but also we need to do more to hold water back, way back in the hills."
He said he understood the impact of flooding on the community, adding: "It is absolutely shocking and horrifying to people's private lives, to their business lives, it is incredibly disruptive."
Ian Liddell-Grainger, Tory MP for Bridgwater and West Somerset, said of the River Parrett: "Once it's dredged we can then maintain it but the Environment Agency has to stop this mucking around and get on with it."
He dismissed as "pathetic" the Environment Agency's claims that the rain would have overwhelmed the river system even if it had dredged the waterways.
"It is an absolutely ridiculous excuse," he said. "This never flooded to this level ever in living memory, and we've got people who have been here for a long time. If you look back into the mists of time you don't have this."
It comes as the National Famers Union in the South West said the floods had left farmers in a state of "utter despair". and the Environment Agency said about 40 properties in the Somerset Levels had flooded.
Prime Minister David Cameron said he thought the Environment Agency had done "excellent work" helping communities deal with flooding.
But he added that it had to listen - and address - concerns over flooding.
BBC weather forecaster Susan Powell said frequent showers from 21:00 GMT through to midnight on Tuesday could bring up to 25mm (1in) of rain in parts of southern England, with a risk of up to 40mm (1.5in) of rain on higher ground in south-west England.
The Environment Agency said there was also "a risk of groundwater flooding in Hampshire until Wednesday" and that "parts of Wiltshire, Dorset, Hampshire, West Sussex, West Berkshire and Surrey may also experience localised groundwater flooding over the next five days".
And the Met Office is warning that persistent rain will fall on to already saturated ground in northern and eastern areas of Scotland creating a risk of localised flooding.
Flood warnings in England are in place for parts of the Midlands, North East, South East and South West. are also more than 140 flood alerts - indicating flooding is possible - in places across England and Wales.
Parts of northern England and Scotland have seen snow, but so far there has been little travel disruption in the majority of the UK, although ferry crossings between Weymouth and the Channel Islands were cancelled due to adverse weather.
One sporting event hit by the weather was the racing at Plumpton, east Sussex, which was abandoned on Monday due to a waterlogged course.