Pound and Euro signs are seen above a cashpoint in London, Tuesday, Oct. 4, 2016. The British pound has hit a 31-year low against the dollar amid concern the country is willing to break away definitively from the European Union's common market. (AP Photo/Kirsty Wigglesworth)

Pound and Euro signs are seen above a cashpoint in London, Tuesday, Oct. 4, 2016. The British pound has hit a 31-year low against the dollar amid concern the country is willing to break away definitively from the European Union's common market. (AP Photo/Kirsty Wigglesworth)

LONDON (AP) — Britain’s main stock market fell agonizingly short of an all-time high on Tuesday amid a groundswell of optimism that exporters and multinationals will benefit from the pound’s woes in the wake of the country’s vote to leave the European Union in June.

The pressure on the currency, particularly against the dollar where it is trading at 31-year lows, has mounted this week following comments from Prime Minister Theresa May that suggested the country could be heading for a definitive break from the European Union’s single market.

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The worry, at least in the currency markets, is that a clean break could threaten the pre-eminent position of London’s financial sector, and see tariffs slapped onto exports and foreign firms like Nissan abandon their British bases.

At one point Tuesday, the pound, which traded around $1.50 on the day of the June 23 vote to leave the EU, fell as low as $1.2720, a level not seen since June 1985, when Margaret Thatcher was British prime minister and London was readying for Live Aid.

The pound is also suffering against all its major competitors, including the euro, which is used by 19 countries in the EU.

The pound’s descent since June means the country is less well-off — British tourists visiting Disneyland in California or Greek islands clearly noticed that their pounds didn’t go as far.

That fact hasn’t equated to lower share prices, though. The main FTSE 100 index, which has enjoyed a sustained rally since the Brexit stage, nearly broke new ground on Tuesday, only to fall around a point short of its record high of 7,122 set in April 2015. The index closed up 1.3 percent at 7,074.34.

The rally is due to the fact that the drop in the pound — while a drag on spending abroad — is potentially good for those British firms that already have huge business interests outside the U.K. And there are a lot of them listed on the FTSE 100.

Exporters will see their goods become more cost competitive in international marketplaces, especially while the country remains within the EU. And the money they make abroad will be worth more when it is brought back to the headquarters in the U.K.

Fashion house Burberry, which sells heavily in the U.S., Europe and Asia, has recently said its earnings have been boosted by the fall in the pound, while warning of challenging times ahead.

Pearson, the education publisher, makes a lot of its money in dollars, and was one of the top risers on Tuesday. It’s the same for miners and oil firms like BP and Royal Dutch Shell, whose products are denominated in dollars. And for industrial names like Rolls-Royce.

“The reality is the biggest stocks in the index dominate its performance, and the likes of HSBC, Royal Dutch Shell, and British American Tobacco all have international earnings which are now worth more in pounds and pence thanks to (the pound’s) decline,” said Laith Khalaf, senior analyst at Hargreaves Lansdown.

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It’s not just the big exporters seeing a rise in their shares this week. Even smaller British companies focused on the local economy are gaining thanks to recent upbeat economic indicators and the central bank’s recent move to cut interest rates.

That’s a marked change from earlier this summer, when domestically focused companies saw their shares dive on concern about an economic recession that has not materialized.

The latest drop in the pound was triggered by comments over the weekend by May, who replaced David Cameron as prime minister in July.

She fleshed out some details over how the country will leave the EU, saying she will invoke by March the so-called Article 50 of the EU treaty, the mechanism by which two years of talks on Britain’s exit officially commence.

She also appeared to signal that her government would prioritize controls on immigration over access to the European single market, an approach informally called a “hard Brexit.”

It remains unclear, however, what the negotiations will ultimately bring for the British economy, though the International Monetary Fund said Tuesday that growth is set to slow sharply in 2017 to a meager 1.1 percent from 1.8 percent this year.

“The truth around Article 50 and a ‘hard Brexit’ is that nobody really has any idea what the outcome or repercussions will be,” said James Hughes, chief market analyst at GKFX.

“So for the markets, it is the utter uncertainty that is causing the volatility and downside movement for the pound, and not any kind of factual information or informed guess work.”