In response, house owners are starting to put up their homes up for rental for just that week, encouraged by the lure of mega rents, possibly up to five times the normal going rate.
Suzanne Coker, who lives with her husband, James, in Barton-on-the-Heath in the Cotswolds, has a large house with an adjoining cottage which she is just starting to let out. "We had considered inviting a few friends up for the millennium weekend and putting them up in the cottage. But we have been told by local rental agents that we could get a very good return and that is just too tempting."
The cottage, which sleeps five, with a large dining room, sitting room and wood-burning stove, is usually let for pounds 350 to pounds 400 a week, but with the possibility of earning at least pounds 800 for that one week, they hope to take a short, but extravagant, holiday later in the year. "We will just stay with friends," says Suzanne.
Although the Cokers are looking at doubling their rent, larger properties are being let for up to five times the norm. Warren de Longe of Blandings, the country-house holiday-rental agent, which is offering a number of properties for the millennium, says: "Most of the larger houses are going to groups of individuals or couples wishing to celebrate the event, rather than families.
"While these groups are often willing to spend greater sums of money, many of our owners prefer families, as they are less likely to bring in the millennium with a `bang'."
The most expensive property the company is offering for the New Year week is Hatton Castle, near Turriff, Aberdeenshire. This has eight bedroom suites, and will cost pounds 55,000 per week, excluding staff. For a little bit less, you could take Braxted Park in Witham, Essex, which is a nine- bedroom country house, at pounds 30,000 for the week.
Then there is St Catherine's Court near Bath, Somerset & Avon, a 14th- century property, which accommodates 16, for pounds 40,000 or, Widecombe Manor in Devon, a 19th-century manor house sleeping 14, for pounds 15,000 - or just over pounds 1,000 a week per person.
Leon Betchley of Countrywide Residential Lettings covers the south coast of England. He says: "I am getting an awful lot of enquiries from the Home Counties and London, especially from large families or parties. Within the last two weeks we have taken 50 enquiries."
He reckons that a four-bedroomed property usually let out for pounds 450 to pounds 500 a week could easily command pounds 1,500 to pounds 2,000, and he is advertising for suitable property. He already has a few houses on his books in the Isle of Wight, and these include Cove Cottage, a three-bedroom cottage at Ventnor; The Barn, a four-bedroom house at Whitwell; and Stoneplace Cottage with three bedrooms at Ventnor. They will all be available for around pounds 800.
Many of the properties already available for renting over the New Year are in Scotland. Robert Rattray of Finlayson Hughes of Perth, which has published a special millennium brochure, says: "We have been inundated with enquiries for large and exclusive venues."
Several of the 16 properties are already booked, and of those still available you could take Burnknowe at Lochgoilhead, Argyll, sleeping eight for pounds 5,000 a week, Denfield Farmhouse in Trinity Gask, Perthshire, for pounds 5,500, or Lochiehead at Auchtermuchty, Fife, sleeping 14, plus four in a cottage, for pounds 12,500 a week.
Knight Frank's Edinburgh office has also been asked by some of its clients to find tenants over the millennium week. Properties up for grabs range from stately homes to castle and shooting lodges. "Some are fully staffed, others are self-catering farmhouses, and packages are being tailored to meet people's individual requirements wherever possible," says Colin Strang Steel.
One property available is Strathtyrum at St Andrews, Fife. Twelve people staying here would have use of the drawing room, library, billiard room and dining room, and the pounds 30,000 for seven nights includes all meals and drink.
Also in Scotland, F D D Savills has several properties available for that week. On the Airlie Estate, for example, Cortachy Castle, which sleeps at least 20 people, is available for pounds 24,000 for four days; and Wellbank Cottage, which sleeps six to eight people, pounds 2,000 for the week.
You should, of course, insure your home while it is rented out over the millennium week. A standard buildings and contents insurance will not cover the property if it is let and anything untoward occurs, and it is unlikely that a high street or telephone insurance company would countenance such an extra liability.
Countrywide say it is encouraging people to take a very much larger deposit than usual - pounds 300-pounds 400, as opposed to pounds 50-pounds 100 - to cover any damage. And it is offering an insurance package covering all liabilities, which will cost around pounds 150-pounds 200, depending on what has to be covered.
Suzanne Coker, 01608 674603; Blandings, 01223 293444; Finlayson Hughes, 01738 451111; Countrywide Residential Lettings, 01983 821111; Knight Frank, 0131-225 8171; F P D Savills, 01356 628600