Police held back the crowds of people and urged them not to "barge through"
Some 900 home and shop owners in one of the towns worst hit by recent flooding have been allowed to return by police.
All properties in Cockermouth are being checked by engineers before people can enter. Elsewhere in Cumbria, at least 25 roads and 16 bridges remain closed.
There are 20 flood warnings across the UK but forecasters say Monday's rain should not raise river levels.
However, more is due on Tuesday and the Environment Agency said it was "keeping a very close eye on the situation".
The Met Office is warning of 70 to 100mm (2.8 to 3.9in) of rain over high ground in Cumbria.
It is expected to start at about 0600 GMT on Tuesday, only dying out at about midnight.
A spokesman said: "It's certainly enough to exacerbate the recovery problems."
Communities minister Rosie Winterton is chairing a meeting of ministers to discuss what more can be done to help victims of the flooding.
'Utterly devastating'
Environment Secretary Hilary Benn told the Commons the clean-up operation had begun in Cumbria but there could be some further flooding on Tuesday.
He said: "I saw for myself on Friday and Saturday in Cockermouth just what an effect the torrent of water had on homes, businesses and communities. It is utterly devastating."
He said that although the flooding could not be attributed to climate change, more extreme weather could be expected in the future.
Mr Benn said a record £2.15bn was being invested in river and coastal defences over three years.
Shadow environment secretary Nick Herbert called for a formal review of flood defences in the area.
Liberal Democrat spokesman Tim Farron, who represents Westmorland and Lonsdale in Cumbria, said the devastation had brought communities closer together.
In Cockermouth, Natalia Ekarad said she was "devastated" by the state of her home in Main Street after returning there.
"We have been here two years and were so happy. Now everything is gone," she said.
Elaine Oxon, owner of fashion store Westmidges, said she had lost her entire stock.
"The smell is absolutely horrendous - it might be contaminated," she said.
"We may never be able to open again and I feel like giving up. Everything is ruined."
River search
Five secondary schools and 13 primary schools in Cumbria remain shut, with many homes and businesses still cut off.
FLOOD ADVICE
Cumbria Police casualty bureau: 0800 0560944 or 0207 1580010
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There are 10 flood warnings in the north-west of England, five in Wales, three in the Midlands, and one each in the North East and Scotland.
There has also been a Met Office warning for localised flooding in western counties of Northern Ireland.
A search has resumed for a 21-year-old woman who was swept along the River Usk in Brecon, Powys, on Saturday night.
A man who was with her raised the alarm. He has been helping police with their inquiries as they try to establish exactly what happened.
Work continues on a safety review of all 1,800 bridges in Cumbria, where six crossings have already collapsed and Calva Bridge in Workington, which is also in danger of crumbling, has been condemned.
Its closure means people in Northside face a 40-mile road detour just to get to the town centre.
Twenty-five soldiers from 39 Regiment the Royal Artillery have been sent to flood-hit areas to assist the emergency services.
'Very traumatic'
Cumbria Chief Constable Craig Mackey said it could take years for Cumbria to recover from the damage.
Cumbria County Council chief executive Jill Stannard, who took up her post only last Thursday, said the damage from the floods had run into "tens of millions of pounds" after more than 1,300 homes were flooded by record daily rainfall last Thursday and Friday.
Liam Dutton with the BBC weather forecast
Ms Stannard said the authorities were trying to establish the whereabouts of people who were unaccounted for, although she stressed many of them might have gone to stay with relatives and friends outside the area.
She told BBC Radio 4's Today programme: "We are confident we can reach everyone. People get very frightened - totally understandably because this is very traumatic.
"It is important that people listen to advice through the media and don't listen to rumour and gossip."
An Environment Agency spokeswoman said the additional rain on Tuesday would fall on already saturated ground.
"We are keeping a very close eye on the developing situation and we ask the public to stay tuned to local radio stations and call the Floodline on 0845 988 1188 for the most up-to-date information," she said.
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I feel like giving up - everything is ruined
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