Brokers report "phenomenal growth", "the fastest I've ever seen" and that "business has exploded". The difference between this and past booms, the privatisations of the 1980s and the building society demutualisations of the early 1990s, is that there are no giveaways on offer. This time, private investors have made their own mind up to buy into the next Microsoft, the new Intel.
One broker, Yorkshare, had its busiest day ever on Wednesday. Customers for Charles Schwab could not get through for two hours because buyers were jamming phones and Barclayshare is turning new clients away, unable to cope with the avalanche of orders for hi-tech and telecoms shares.
The facts of the month-old frenzy are simple. Brokers' systems are buckling under the pressure, so Britain's senior financial regulator, the Financial Services Authority (FSA) is launching an investigation. Even ProShare, the organisation which encourages wider share ownership, yesterday warned private investors to be wary of trading in the frenzied conditions.
Tony Hobman, chief executive of ProShare, said: "People should trade in shares only when the conditions are right for them." He had been told of private investors trading in shares using as little as pounds 100 in any one deal. Brokers' fees and stamp duty will quickly cut that to around pounds 80 at a stroke. ProShare recommends a minimum investment of around pounds 500 for each deal.
Chris Ring, managing director of NatWest Stockbrokers, harassed but exhilarated, said: "Over the last month volumes have doubled. Clients are snapping up all the hi-tech and AIM stocks but, interestingly enough, one of our top purchases remains Marks & Spencers. We've seen high sales when the building societies demutualised. But we've never seen such a sustained high volume of purchases. Its a sea change in private investor behaviour."
NatWest is taking more people on to cope with the increased business, taking orders and dealing, even drafting staff in from other parts of the bank. And Mr Ring sees no immediate end to it. "If the market keeps going up, with no setbacks, volumes could still increase. I expect that in the day and a half trading between Christmas and New year, the New Year tips in the papers could spur a further frenzy."
The Big City institutions look set to join in the race to "build the new economy" as Internet boosters put it.
But he warned: "Before the end of the year, liquidity in the market provided by the institutions in the next couple of weeks could dry up because of millennium fears. So the spreads facing private investors (the difference between a share's buying price and selling price) could be as wide as a London bus". He says it is vital to give your broker a price limit - saying, for example: "Don't buy above x, don't sell below y."
Paul Howard, product development manager with Yorkshare, an execution- only stockbroker in Bradford, says sales to private clients have "exploded". He added: "Tuesday was our busiest day ever. Sales have doubled in two months and we've had to recruit an extra 40 staff to add to our existing 100. Even after that we're still finding it hard to keep up with demand."
Yorkshare was launched by the Yorkshire Building Society in February 1994 and was bought from the Society last month by the world's second largest execution-only broker, the giant American company TD Waterhouse. This reflects the growing American opinion that its own appetite for share- dealing by individuals is finally catching on in a really big way Over Here.
"Many people are buying Techmark stocks," says Mr Howard, referring to the London Stock Exchange's hi-tech index launched on 4 November. Since then, Techmark has rocketed 38 per cent. He believes the private investor frenzy has been fuelled by TV programmes such as Show Me the Money, a penny share-tipping programme shown daily on Channel Four which has just finished a 13-week run. Teams of three take a notional pounds 100,000 pot and attempt to beat each other by picking penny stocks.
Terry Bond, an experienced private investor who writes a regular column for The Independent (see page 5), is worried by the way the show has been able to send shares soaring in minutes. "As soon as the market makers in the City see what's being tipped, they mark up the price," he says. The programme caught the public's imagination in a way not seen since the building societies started demutualising when millions of new shareholders were created.
Mr Bond repeats ProShare's warning. "People must look at the spreads of these penny stocks before investing. With stockbroker's charges, the spread can wipe out your profit with penny shares very easily."
At Charles Schwab, the giant US brokerage making waves in the UK, customers wanting to buy shares are being put on hold for up to two hours because there are not enough phone lines to handle the avalanche of calls. Schwab is hurriedly recruiting staff at its Birmingham head office to plug the gap. Guy Knight, European marketing director at Schwab, says business has been "just phenomenal".
Schwab publishes a Top Ten "buys" and "sells" each Thursday. This week the most bought share was "365 Corporation", an online sports and lifestyle content provider. Its shares have soared 77 per cent since its stockmarket debut a week ago. The top seller was BT, the copper-wire based dinosaur. But is all this frenzy - and discounting market hype, everybody The Independent spoke to agreed this is a frenzy - creating a bubble? Will share prices get out of hand, to be punctured when enthusiasm and/or cash runs out, perhaps sometime next year?
Brian Tora, chairman of the Investment Strategy Committee at Greig Middleton, a private client stockbroking firm, remembers only too well the last stock market crash 12 years ago. "The savage correction that took place in the second half of October 1987 appears as a small blip in a driving bull market that has continued now for two decades. But there are similarities between the period in the run up to Black Monday and the present which I find just a little disturbing."
And he warned too: "Deep down inside I feel it could all end in tears, but there are plenty of professional managers that are riding this particular bandwagon, because to ignore it could prove even more dangerous.
"There is no doubt we are in the middle of a revolution, the like of which none of us in the City have experienced. But I fear more than a few people will be severely financially damaged when it settles down."
So how long should you ride this particular Tiger? Mr Tora says: "If we sail through Y2K (the millennium bug syndrome) without too much of a blip, then this surge in prices may well continue."
This late surge should give you an opportunity to sell out before the chances of a crash increase, he says. The traditional stockmarket saying, "Sell in May and go away" could prove sound advice again.
John Willcock is The Independent's Personal Finance Editor