LONDON — Britain’s top stock market index, the FTSE 100, struck a record high on Tuesday amid hopes that many of its listed companies will benefit from the pound’s slide in currency markets.

While the pound has tanked following the June vote to leave the European Union, the FTSE 100 has surged. On Tuesday, renewed worries over the cost of Brexit piled pressure on the pound, pushing the stock index to an all-time high of 7,129.83. It lost some of those gains later, to close down 0.4 percent at 7,070.88.

At first glance, the stock gains since the June 23 referendum may appear perverse — after all, the fall in the pound indicates that investors are less hopeful about the British economy as the government looks to break away from the EU’s single market.

But the pound’s decline, while a drag on British spending abroad, is potentially good for British firms that already have big business interests outside the U.K. And the money they make abroad will be worth more when it is brought back to the U.K.

There are many such international companies in the FTSE 100, from oil giants like BP and Shell to educational publishers like Pearson and fashion houses such as Burberry.

As the pound drops — it’s fallen around 20 percent since June 23 — exporters have seen their goods become more cost competitive in international marketplaces.

“Brexiters might point to the FTSE’s rise as a sign of strength but this is very much a story of (pound) weakness boosting foreign earnings, which account for around two-thirds to three-quarters of FTSE 100 company revenues,” said Neil Wilson, markets analyst at ETX Capital.

While the pound’s slide against the dollar has captured most of the headlines, especially Friday, when it plunged about 6 percent at one point to a 31-year low of $1.1789, the currency is posting equally dramatic declines against the euro, which is used by 19 EU countries. One euro is now worth 0.90 pounds compared with around 0.76 pounds just prior to the Brexit vote result.

The irony of the pound’s dramatic fall is that it will help British businesses secure market share in the EU’s single market, of which Britain is still a member until at least 2019, by making their goods more competitive.

Having suffered an immediate slide in the wake of the Brexit vote, the pound settled for much of the rest of the summer. But that changed at the start of this month when the government of new Prime Minister Theresa May started to lay out its vision for Brexit.

May, who replaced David Cameron in July, said she will invoke by the end of March the Article 50 of the EU treaty, the move that will officially start two years of talks on Britain’s exit. She also signaled that her government would prioritize controls on immigration over access to the EU market that is so valuable to many British companies.

A report in The Times newspaper on Tuesday, citing leaked papers from the Treasury department, said a so-called “hard Brexit” could lead to government tax revenues collapsing by 66 billion pounds ($81 billion) a year and that the country’s GDP could be 9.5 percent smaller if Britain leaves the single market and operates under standard World Trade Organization rules.

The report helped put further pressure on the pound. Add the uncertainty related to the Brexit negotiations and the Bank of England’s policies, which could see interest rates cut further, and the outlook remains bleak for the pound.

If not necessarily for stock portfolios.