English Nature, the Government's wildlife conservation arm, is in dispute with the owners - the Christie family, who founded Glyndebourne opera - and the Ministry of Defence, over the management needed to preserve their rare and beautiful plantlife.
The burrows, on north Devon's Taw and Torridge estuary, have almost every kind of official designation. They are a National Nature Reserve and a Site of Special Scientific Interest within an Area of Outstanding Natural Beauty and a Heritage Coastline. They form one of England's three Unesco World Biosphere Reserves.
The dunes are open to walkers and are also an infantry training ground, but the plantlife can cope with those uses. The threat comes from an invasion by scrub - brambles, privet, birch and willow. The thin carpet of wildflowers, many of them rarities, which turn the dunes bright purple and yellow in midsummer, is being swamped.
English Nature staff want to graze the entire area with hardy sheep and cattle to hold back the scrub. But the organisation has not obtained permission from the Christie family's estate, or from the Ministry of Defence, which leases it for training. All three profess concern about the scrub. English Nature staff say that the estate and the ministry have dragged their feet and gone back on agreements; the estate says the same of English Nature.
The conservation organisation itself is divided on the issue, with some staff feeling its negotiators should take a tougher line. But English Nature's sub-lease from the Ministry of Defence expired in 1984 and it is there by grace and favour.
The burrows, the second largest area of dunes in England, are naturally in a state of flux as sand is blown inland. On the seaward side there is bare sand and marram grass. Further inland they are covered in 'thyme turf', a mixture of small plants including thyme and kidney vetch adapted to the poor soil and harsh conditions. It is this that is being overcome.
Once, rabbits kept grass and scrub at bay but their numbers were drastically reduced by myxomatosis in the 1950s. The dunelands are also drying out, probably because of improved drainage of adjacent farm land and irrigation of a golf course.
English Nature is allowed to graze 70 hardy Soay sheep on 30 acres of the reserve. This flock has shown that grazing can hold back the scrub and now the organisation wants to graze hundreds of sheep and cattle over all 1,500 acres.
But Charles Coldwell, the estate's land agent, said the trampling of cattle would damage the land. The drinking ponds that would have to be dug would further lower the water table. Last year English Nature had not responded to an offer for soldiers to clear some of the scrub, he added. 'Something has got to be done and nothing would delight me more than reaching an agreement. The Christie family have conserved this land for decades and they want to continue to do so.'
Dr Robert Walton, of English Nature, said: 'We're deeply worried that one of the finest sand-dune systems in Europe is scrubbing up through lack of grazing.'