By Guy Faulconbridge

NEW YORK (Reuters) - British Prime Minister Theresa May met business chiefs from firms including Goldman Sachs <GS.N>, IBM <IBM.N> and Amazon.com <AMZN.O> on Monday in an attempt to reassure investors after her country's shock vote to leave the European Union.

The June 23 vote took many investors and chief executives by surprise, triggering the deepest political and financial turmoil in Britain since World War Two and the biggest ever one-day fall in sterling against the dollar.

"Every working day in the United Kingdom one million people wake up and go to work for an American company. And every day in the United States one million people wake up and go to work for a UK company," May told the business leaders.

"So you see there is reciprocity," said May, who is in New York to attend the United Nations General Assembly. "The UK is going to be out there. We will be looking ‎for business. And ladies and gentlemen, please feel free to invest in the UK."

May said that she wanted to hear what issues business leaders wanted addressed in the Brexit negotiations, which she said would yield a good deal in the trade of goods and services with the EU.

Chief executives from AECOM <ACM.N>, Morgan Stanley <MS.N>, BlackRock <BLK.N>, Merck & Co <MRK.N>, Sony Pictures and United Technologies Corp <UTX.N> also attended the meeting.

The head of Thomson Reuters <TRI.TO>, the parent company of Reuters News, also attended. May first had a closed meeting with major investors and Wall Street banks before addressing dozens of other executives at a wider reception.

Despite warnings before the vote that Brexit would shatter economic confidence, some positive economic data and SoftBank's $32 billion takeover of Britain's technology company ARM have stoked the perception that Britain could prosper outside the EU.

Still, May and her ministers admit they need to reassure investors from the United States, Japan, China and India that the United Kingdom and London, the only financial capital to rival New York, are still good places to make money.

The United States is the largest single inward investor into Britain, which currently attracts far more foreign direct investment than any other EU member.

When asked what they wanted to hear from May, one business leader at the meeting who asked not to be named said: "Reassurance."

"BREXIT MEANS BREXIT"

Some investors have called for clarity about how much access foreign companies based or operating out of Britain will have to the European market, a concern for some U.S. banks and manufacturers which sell into the EU from Britain.

Other issues include when and how Brexit will happen. May, who has repeatedly pledged that "Brexit means Brexit", has so far said only that she will not trigger the formal EU divorce process before the end of this year.

"‎We will be getting the right deal for the United Kingdom and that is the right deal in terms of trade in goods and services because we recognize the importance of both," May said.

"At the same time we want to scope out new deals around the world to further liberalize trade between the UK and other partners around the world," she added.

U.S. President Barack Obama said this month that he wanted the Brexit process to be resolved in the least disruptive way possible, though both France and Germany face elections next year which could complicate the Brexit negotiations.

Before the vote, some U.S. companies had warned that Brexit would complicate their lives and could cost jobs. Those included JPMorgan Chase Chief Executive Jamie Dimon, who has 16,000 staff based in Britain.

British companies reduced their investment plans in the month after Britain voted to leave the EU, a survey by Lloyds Bank showed on Monday, a further sign the decision is likely to have a lasting impact on the economy.

Last month, the Bank of England left its forecast for British growth this year steady at 2.0 percent but cautioned that there might be little growth in the second half and sharply downgraded its forecast for 2017 to just 0.8 percent from a previous estimate of 2.3 percent.

"What I really wanted to talk to you about tonight is just very simply to say this: Britain is open for business," May said.

(Reporting by Guy Faulconbridge; editing by Chizu Nomiyama, Grant McCool and Bill Rigby)