The FTSE 100 share index has risen above 7,100 for the first time since April 2015, as sterling fell to a 31-year low against the dollar.
London’s leading share index jumped 1.8%, or 126 points, to 7,110 – above its previous record close of 7,103.98.
However, the pound fell to $1.2737 at one point – its lowest level against the US dollar since 1985.
Sterling has fallen for the past two days as traders study the Conservative Party conference for Brexit details.
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The pound was down 0.3% against the euro at €1.1424.
The FTSE 250 share index, which features more UK-focused companies, was at a record high of 18,590 points – up 2.2%.
Stock markets in Frankfurt and Paris were also higher on Tuesday.
The FTSE 100 has benefitted from the fall in the pound since the Leave vote because the many international companies whose shares are traded in the UK tend to benefit from it.
Profits earned abroad by multinationals such as drugs giant GlaxoSmithKline and major mining companies are worth more when converted into sterling.
That makes a company’s shares appear better value when compared with the higher profits it will make, prompting a revaluation of the stock.
The FTSE 250 index, however, has lagged behind the FTSE 100 since the Brexit vote because gains from the weaker pound for the outward-looking businesses have been offset by fears about the fortunes of UK-focused companies.
The FTSE 250 contains a higher percentage of UK-facing businesses than the 100. Since June though, a string of better-than-expected economic news has also helped to lift their share prices.
On Tuesday, a closely watched survey suggested that the UK’s construction sector had unexpectedly returned to growth in September.
The latest Purchasing Managers’ Index for the construction sector rose to 52.3 from 49.2 in August. Any figure above 50 indicates expansion.
“Resilient housing market conditions and a renewed upturn in civil engineering activity helped to drive an overall improvement in construction output volumes for the first time since the EU referendum,” said Tim Moore, senior economist at IHS Markit, which compiles the survey.