Sterling slid to its lowest in more than three decades on Tuesday on fears of a "hard Brexit" from the European Union and its single market that could hurt the economy, although the weaker pound sent U.K. stocks surging.

The pound has already lost 1.7 percent against the U.S. dollar since Prime Minister Theresa May said on Sunday the formal process to take Britain out of the EU will start by the end of March 2017. On Tuesday, she added the divorce from the EU will not be "plain sailing" and that there would be "bumps in the road."

Many economists and investors fear May's government will back a "hard Brexit" option where Britain quits the single market in favor of imposing controls on immigration.

That could hinder inward and outward trade and constrict the foreign investment needed to fund Britain's huge current account deficit, one of the biggest in the developed world.

Economic activity has held up better than many had expected since Britons voted in a June referendum to leave the EU, but many policymakers are anxious about the prospects for future investment. The Bank of England launched a big stimulus package in August and may ease policy again in coming months, which could drag the pound still lower.

"Most of the key (BoE) members have expressed a willingness to continue acting pre-emptively ... and an expectation that more easing is likely to be necessary," UBS strategist John Wraith said.

"Additional stimulus would likely drive further sterling weakness," he said, reiterating the bank's forecast for $1.20 per pound and parity with the euro by end-2017.

The pound extended losses on Tuesday, slipping more than half a percent to $1.2737, its weakest since mid-1985. It also hit a three-year low of 87.65 pence per euro , down 0.2 percent on the day.

The nervousness in the spot market led to a rise in the cost of hedging against sharp swings in the currency in the next three to six months.

The cost of hedging sterling exposure against the dollar for six months -- which includes March, when May says Brexit will begin -- was at 10.60 percent, the same as the nine-month option. Typically a nine-month currency option is dearer than a six-month one.

STOCKS SOARING

The pound's tumble boosted British stocks, however, with the market also taking heart from soundings from UK factories last month that indicated the economy was still on track for robust growth in the third quarter.

With the cheaper currency promising to bolster earnings and enhance competitiveness, Britain's FTSE 100 index rose above the 7,000-point level for the first time since mid-2015.

The blue-chip index has risen more than 11 percent since its pre-Brexit level and is within striking distance of its historic high of 7,122.74.

Even more heartening for investors has been the rise in the domestically exposed FTSE 250 index of mid-sized British firms, which hit a record high on Tuesday having gained around 6.5 percent since the referendum.

The mid-caps have benefited from upbeat data and surveys of British households and businesses that have led many forecasters to drop predictions the economy will slip into recession this year. U.S. investment bank JPMorgan, for example, doubled its third-quarter GDP forecast to an annualized 2 percent last week.

Analysts also cited the prospect of further acquisitions as foreign buyers take advantage of a cheaper currency to scoop up U.K. companies.

"There's certainly a perception that, as you go down the market cap range, the potential list for takeover targets gets a bit longer," said Ian Williams, economist and strategist at Peel Hunt. "And, of course, for foreign investors who are looking at sterling-denominated assets, they are continuing to get a bit cheaper."