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.