A large proportion of hotels and restaurants have already decided to close their doors. Public transport may not run. And, most worryingly, hospital emergency departments may not be able to function because of the difficulty of getting staff to work the festive period without substantial financial inducements.
Little thought was given to such matters when the big party venues started selling out long before Mr Heseltine spoke those words. The Royal Albert Hall was booked for New Year's Eve 1999 in 1975. Madame Tussaud's and Tower Bridge were snapped up long ago. The Queen Elizabeth II has been grabbed by the Millennium Society of Washington for a 20-day cruise at an estimated pounds 300,000 a day, and DisneyWorld, in Florida, has sold out its 17,000 hotel rooms. British Airways will not start selling tickets for Concorde until 11 January but the price is likely to be "very high" said a spokeswoman.
Edinburgh has announced its Millennium Hogmanay will be extended to seven days from the normal four. The concert will have a "big name, preferably with a Scottish connection - someone like Rod Stewart" said a spokeswoman, and there will also be more street theatre and other events. Because of public safety restrictions however there will be the same number of tickets for the street party as usual - 180,000 - so trying to get hold of one will be more difficult than ever.
The Millennium Dome has not yet announced what form its event will take, but a spokeswoman said that it would not be open to the public. It will be for VIPs and invited guests, although some people will be able to win tickets through competitions in the media.
At the Millennium party, everyone wants to be the guest and no one wants to be the worker. So caterers, taxi companies, childminding agencies hotels and restaurants are facing the dilemma: can they afford to pay staff the fat bonuses they will demand? And even if they do offer more cash, will 31 December 1999 see unprecedented outbreaks of "food poisoning", "flu" and other inventive excuses?
The British Hospitality Association polled its 25,000 members and found that a quarter of hotels and restaurants will not even bother to open on New Year's Eve 1999, and a further 17 per cent are still undecided. Those that do are likely to charge a hefty mark-up on normal prices, says BHA chief executive Jeremy Logie. Nearly one in six establishments have decided to charge 100 per cent more than their normal New Year's Eve rates, and 28 per cent will be charging between 50 and 100 per cent more.
Catering is not a bad job to be doing on New Year's Eve, argues Mr Logie. "You're involved in the party, and that can be very exciting. You may not actually be revelling but you're with the revellers. It's got to be a better job than driving a bus." Mr Logie said the main problem managers would face, though, was whether staff would bother to turn up to work at all.
"There's going to be an awful lot of people calling in sick," predicted a spokesman for Reed Employment. This year, it says, there were nine days in December when there was not enough catering staff to go round, compared to two days last year. It expects next year's figure to go even higher. "The rumour is going round that staff will expect pounds 1,000 for a night's work, but we're not sure about that," said a spokesman. "But we do expect that staff will be paid four to five times their normal rates."
Those with young children will be particularly hard hit. Childminders, the world's largest baby-sitting agency, says it will charge pounds 40 to pounds 50 per hour on the night. "But we anticipate little demand," said a spokes-man. "We've had a lot of inquiries from the media but not one from anyone actually wanting a baby-sitter.
Then there's getting home. Trains usually stop at 10pm on New Year's Eve - next year rail companies will need to apply to Railtrack if they want to offer a later service. London Transport's plans are not yet finalised. "We're negotiating with staff," a spokesman said. It is thought that the bill for keeping the system running on New Year's Eve (usually met by private companies) could treble to pounds 700,000 for the Millennium. Police have warned that the system might have to shut rather than risk chaos with an under-staffed and incomplete service.
The usual alternative would be to take a cab. But Derek Myers of Computer Cabs, which has 2,500 taxis in London, is scarcely more comforting. He says the company is planning a poll of drivers to see who is willing to work on Millennium Night. "The demand for cabs could be monstrous," he says, "but we're unsure how many drivers will be willing to work and our regular account customers will be the priority."
Inevitably, with so many people going out to celebrate, there will be accidents. So for police officers, firefighters, medical and ambulance staff it will be work as usual. But health chiefs are worried that it will be impossible to staff emergency services because domestic and ancillary staff will be reluctant to work. Barry Elliott, director of finance at the Royal Hospitals Trusts, says that there could be a "bidding war" between hospitals for staff.
"It is our biggest problem," Mr Elliott said. "Problems to do with the year 2000 with computer systems or medical equipment are being taken into account but we don't know how we are going to effectively staff emergency hospital services over the period.
So the safest thing to do next New Year, however boring it may sound, is to celebrate at home. But if you do, make sure you have stocked up. While Asda and Safeway say they have yet to make up their minds, Sainsbury's has decided that its 394 stores will close from 6pm on 31 December 1999 until 3 January. Get the whisky, coal and haggis in early.
Travel, page 5