Thieves have been targeting flood victims on the Somerset Levels, police said.
Around 600 gallons of domestic heating oil was stolen from a farm in Moorland overnight from Friday to Saturday.
Two fire service quad bikes were taken from Burrowbridge on the same night.
The national police air service (NPAS) helicopter flew over the flood-hit area as a "proactive crime prevention exercise".
Police horses have also been deployed and officers will make regular patrols for a "high-visibility presence" and to reassure residents.
Four extra high volume pumps requested from fire and rescue services around the country have arrived on the Levels, adding to the eight already in use.
Currently, the combined pumping across the moors is enough to fill an Olympic swimming pool every 90 seconds.
Chief Superintendent Caroline Peters, of Avon and Somerset Police, who is heading the response to the floods major incident, said: "We are aware of reports in the community of suspicious people and vehicles being seen in the area, particularly after dark.
"We have also heard rumours of people being out in boats at night, but at this stage we have no information to substantiate that.
"Our message to the community is that we will do all we can to protect you and your property. I would ask everyone to be alert, to look out for your neighbours, and to call us at any time if we are needed."
Special Constables and extra neighbourhood officers from the force have been deployed to the area following thefts, believed to have occurred overnight from January 31 to February 1.
Farmer James Winslade said his home had been left without heating or hot water after thieves stole "more than half" the oil from his tank.
"Because they'd turned it off, that's damaged the pump so now we're without heating and waiting for an engineer," Mr Winslade told the Western Daily Press.
"The problem is that we're getting so many flooding tourists and sightseers coming down here that it's hard to keep track of who's around.
"We've had the fire and police down here a lot, too, but at night it's very isolated. Some of the homes that are empty are being targeted and they are coming across the water on boats to get to them."
On Sunday, volunteers went from house to house on the Levels to check on residents and enquire whether they had concerns or needs such as for fuel and water.
A spokesman for Avon and Somerset Police said the force was looking to help to arrange weekly community meetings, where people can ask questions and be kept up to date with developments.
The South Western Ambulance Service NHS Foundation Trust has installed a public access defibrillator in the church hall in Muchelney in case of medical emergency, he said.
"We're asking people not to be flood tourists and not to travel to the Somerset Levels if they don't have a legitimate reason," the force spokesman added.
"It can hamper the work of the various agencies here, and can actually put people in danger."