It ended nearly 53 points higher at 4,739.6, easily beating the previous all-time high set on 16 May in post-election euphoria.
In the US, the Dow Jones index was 86 points higher at 7,565 by late morning, following the new records set on Friday and Monday. The Dow has gained more than 1,000 points this year.
By contrast, stock markets in continental Europe were quiet and flat as investors decided to wait and see what becomes of prospects for the single currency as a result of the new hurdles thrown up by the French government this week. Shares in Paris suffered slightly more, the CAC 40 index closing 22 points lower at 2,664.18.
Paul O'Connor, an equity strategist at BZW, said the biggest reason for London's advance yesterday was the rise in Wall Street. But he added: "A lot of people are rotating out of the continental European markets, at least in the short term."
Wall Street has been boosted by the diminishing fears that the Federal Reserve will raise interest rates again when it meets in July. In particular, figures on Friday showed that the increase in non-farm employment last month was, at 138,000, far lower than expected. The figures suggested that the US economy is sustaining its astonishing mix of buoyant growth and low inflation.
Although Wall Street was the main explanation for yesterday's soaring share prices in London, they are also expected to be supported by this year's building society flotations.
Market report, page 27