The wildfowlers' speedboat capsized in the swollen river Bann near Coleraine, Co Londonderry. A fourth man managed to swim ashore.
A helicopter was called in to help search for survivors but as darkness fell there was no sign of the men.
Friends named them as Des McGrellish, 31, John Douglas, 24, and Norman Harbinson, 30, a water bailiff on the river, all from Coleraine. Dessie Quinn, 28, also from Coleraine, struggled ashore to raise the alarm. He was treated in hospital for shock and hypothermia.
On the swollen river Conwy near Betws-y-coed in north Wales, three canoeists were swept downstream after an RAF rescue helicopter scrambled to help them was forced to land in a field after flying into a snowstorm. Two of the canoeists reached the bank while the third was carried to the bottom of a 60ft gorge where he was brought to safety by a mountain rescue team.
The London Weather Centre said the rain was steady and persistent, with up to 25 millimetres predicted in places. Heavy showers were predicted for today.
The National Rivers Authority put flood warnings in place on rivers across much of Hampshire and parts of Kent and Sussex.
Widespread flooding of minor roads was reported in Lancashire, and Cumbria police said driving conditions were difficult in lashing rain on the M6, where heavy traffic was heading back from Scotland after the new year celebrations.
In Northern Ireland, the RUC urged motorists to drive only if necessary because of treacherous conditions caused by surface water turning to ice. Many roads were closed by flooding, particularly in Co Down and Co Antrim.
Meanwhile, it was estimated that flood damage caused to the Cornish fishing village of Polperro last Thursday could cost pounds 1m to repair.
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