The strategists said they were concerned that the 10,000 barrier would be seen by traders as a trigger point to sell. As they spoke yesterday the FTSE 100 began to tumble, ending at 6,140.6, down 61.3.
"If the Dow stays there it will help the market. But the feeling is that this represents the high-water mark, the last hurrah of the bull market before it all settles down," said Gareth Williams of ABN Amro, the Dutch investment house.
"It is always helpful to see the Dow doing well. But the concern is that it might signal something of a selling point."
Merrill Lynch, the giant US investment bank, is forecasting a rise of just 3.7 per cent in the FTSE by 31 December. By the end of 1999, the bank forecasts, it will have grown from 5,882 at the start of 1999 to 6,100.
The forecast paints the gloomiest picture for UK stocks since 1994, when the "tequila effect" of the Mexican currency devaluation gave the market a headache, causing the FTSE to slip slightly over the year.
Most experts resist the idea of a 1987-style correction, but they are becoming increasingly worried that the markets have become complacent about the outlook for interest rates.
Philip Wolstencroft of Merrill Lynch said: "The problem is in the US rather than the UK. The US economy has grown like an express train and there are increasing signs that the world economy is also picking up.
"That seems like good news, but it may cause interest rates to rise, making the market's valuation [of stocks] look overstretched. The market has so far managed to ignore that."
Valuations of US stocks now look much more overstretched than those in the UK, according to the strategists. The UK's leading stocks enjoy record high valuations, with investors paying a multiple of 24 times historic earnings. But in the US the multiple is more than 30 times.
The fear is growing that sky high valuations are being supported not by the economic outlook but by a surge of liquidity in the market. Retail investors, suffering low interest rates on cash savings, have been pouring their money into PEPs ahead of their abolition next month.
Robert Buckland, strategist with Salomon Smith Barney, said: "Money is still pouring into the market because of this crazy PEP season. The interest- rate environment looks a bit better than in the US. Because the economy is weaker, interest rates are lower."
The strategists now agree that the boom years of 1996 and 1997, when leading stocks surged by more than 20 per cent a year, are unlikely to return. But highly priced stocks must be set against the background of interest rates.
"It used to be normal for UK interest rates to peak at 17 or 18 per cent. Now they have just peaked at 7.5 per cent. Clearly, something different is going on," said Mr Buckland.