The index closed 22.9 points higher at 4015.1, having pushed through 4,000 in the opening minutes of trading. More than 750 million shares changed hands, in heavier trading than in recent weeks when rises have often reflected dealers squaring their books rather than much underlying demand.
Shares were given a boost by falling bond yields as confidence grew that interest rates in the UK were not about to rise and expectations that rates in Europe had further to fall.
Attention focused on where the market would head now it had broken through 4,000, with the debate in the City hotting up between bears, such as PDFM's Tony Dye, who have staked their reputations and billions of pounds of their clients' money on a large correction, and those who believe the market has further to go.
Peter Sullivan, a strategist at Goldman Sachs, said: "There are two conflicting forces at work. Market valuations look above any estimate of fair value, but against that there is a very positive economic outlook with above- average growth and lower-than-average inflation."
He said markets often remained either above or below fair value for extended periods. Goldman Sachs expects the market to be slighter lower in 12 months' time at 3,950 but does not rule out further rises in the short term.
On the basis of Goldman Sachs models, the London market is, on some measures, more expensive than when it peaked in July 1987, just before the crash that October. The average prospective price/earnings ratio of 15.2 compares with 14.7 in July 1987 and a long-term average of 12.6.
The New York Stock Exchange lifted further into record territory yesterday. The Dow Jones industrial average closed up 29 points at 5,933.97.