The warning follows a spate of break-ins at churches in the south-west of England. Previously thieves have tended to concentrate on stealing church ornaments, such as crosses and chalices.
But in the past few weeks furniture has been seized from more than two dozen remote churches in the West Country. In one police division, north Devon, 28 churches have been broken into so far this year.
Some of the items stolen from the churches in north Cornwall and north and mid- Devon may have been sold abroad, particularly to the United States, the Devon and Cornwall police believe.
Ornate tables and chairs were among many items taken from the churches while they were open to the public.
The recent theft of a 19th- century dark oak chair worth pounds 1,500 taken from St Mary's at Molland, near South Molton, north Devon, was the latest in a series of raids on four parish churches under the Rev Bob Shorter.
Thieves had struck five times in three years at his four churches on the edge of Exmoor, taking furniture including a captain's chair, two Victorian side-tables and a Victorian chest of drawers, together worth hundreds of pounds.
"It does rather appear thieves are coming looking for stuff that they presumably have a market for. Churches are easy targets - and most of us feel you cannot get much lower than stealing from a church," he said.
He had been told that thieves sometimes posed as visitors to see what was in the church, before returning to steal.
"So far our churches are left open and we are reluctant to lock them, but we are now having to think more about that," said Mr Shorter.
In recent years churches throughout the country have suffered from an upsurge in thefts.
In Norfolk, where there are a large number of isolated churches, some of the stolen goods have been traced to antiques markets aboard, including a stained-glass window that was recovered in Japan.
Chief Supt John Savage, of Norfolk constabulary's crime prevention unit, said: "We have a lot of medieval churches, which contain very old and valuable furniture.
"Break-ins can hit small village communities very hard - it's rather like an assault on them."
In Suffolk the police published a crime-prevention booklet for vicars and church wardens following a spate of thefts. Since improvements to security the number of break-ins has fallen dramatically.
Country churches were a favourite target for antique and furniture thieves, said Brian King, of Ecclesiastical Insurance, which covers 95 per cent of Anglican churches.
"Since the 1970s antiques prices have rocketed, therefore churches have been attracted thieves' attention as being a good source," he said. Much of what was taken was sold abroad. Attacks on churches had risen, with insurance payouts rising from pounds 3m in 1989 to pounds 4.5m by 1992. Mr Shorter recommended security marking and photographing valuables; putting fakes on display instead of the originals, or locking them away altogether.