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Rake, the chairman of Britain's BT Group, told CNBC's "The Rundown " that whether the U.K. slipped a small recession or a larger one would likely depend on how quickly it managed the uncertainty following June 23's referendum vote to leave the European Union (EU).
"It is a absolutely critical that we have a leader that stands up, listens to the business community, recognizes what the people of Britain said they wanted and negotiates..with the European Union to get the best possible deal that we can, that benefits both the United Kingdom and the euro zone," he said.
Rake said the ruling Conservatives needed to to quickly choose a leader.
"The Conservative Party must then - with the Opposition, I hope - sit down and develop a strategy for what is the best possible solution for the U.K.," he said. "Is it, for example, a Norwegian option? Can we stay in the single market without full influence but can we at least have access? What exactly is it we are going to propose to engage with the EU?"
"It's critical we have government engage in proper negotiations with the EU because what we need to see is continued access to the single market," Rake added, noting that one of the pressing tasks awaiting the government was to renegotiate trade treaties, which it had not done on its own in more than 40 years.
In the meantime, foreign investors, such as those in U.K.'s motor industry, would likely stay on the sidelines, he said.
"When you have this level of uncertainty and volatility, people are going to wait before they make investment decisions…there's an inevitability of wait-and-see in relations to projects," he added, pointing out that 70 percent of investments into the U.K. were made because it was seen as "the runway to Europe."
Rake was one of one of 1,280 U.K. business leaders who earlier signed a letter backing the remain camp.
U.K. Prime Minister David Cameron announced his intention to resign shortly after the leave result emerged on June 24, saying that his replacement would manage the Brexit negotiations.
But Cameron's Conservatives face an uncertain leadership contest, amid speculation that even key leave campaigners such as former London Mayor Boris Johnson may be reluctant to take on a role that would require triggering Article 50, which is part of the treaty that binds together the EU. Once Article 50 is triggered, the U.K. would have a two-year deadline to complete its withdrawal from the EU.
Cameron met with EU leaders on Tuesday but they were reportedly frustrated by his refusal to immediately initiate exit proceedings.
Meanwhile, the opposition Labour Party is in disarray, after Members of Parliament in the party on Tuesday passed a motion of no confidence in leader Jeremy Corbyn. Many had criticized Corbyn for not campaigning aggressively enough for the remain campaign. But Corbyn said he would not resign and would stand again if Labour called a leadership contest.
Telecommunications giant BT Group employed 81,400 people and owned 7,000 properties in the U.K. and while the company did not plan job cuts in the aftermath of the vote, it was concerned about losing access to manpower from Europe because its current high-speed broadband expansion plan faced labor shortages, Rake said.
"It's therefore essential that we have access to single market in order to roll out this super fast broadband," he said.
He noted that with 80 percent of BT's business being U.K.-related, the Brexit-related hit to its share price was a worry, as was the fact that it had a large company pension fund that it needed to protect. BT's share price has dropped about 17 percent since the Brexit vote,
He said he was also concerned about deep divisions in British society, as reflected by the results of the vote.
"We need to remember...that the large number of people who voted to leave really felt left behind by the U.K. economy and this was in a sense a protest vote, a vote against the establishment and we have to understand that," he said.
"Unfortunately, I do think there was a large amount of exaggeration on misrepresentation, on key facts, particularly around immigration that kind of influences this vote.
"As an individual, I'm deeply upset by the position that has been taken. I think we are all deeply concerned about the divisions in society that we see as a result of this vote, which you can clearly see by the voting patterns and I think we really need to see very strong political leadership to bring this together and for the U.K. to be the kind of country we want it to be, which is a liberal, open country operating in the global, integrated marketplace."
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