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Brexit 'trickle-down' effect could harm consumers, Liberty Global's Mike Fries says

If Britain's transition out of the European Union manages to steer investment and industry away from the U.K., consumers could take the fall, Liberty Global CEO Mike Fries told CNBC on Wednesday.

"My concern is that consumers start to bear the brunt of this a little bit. If people stop investing, if industry slows down, then there's a trickle-down effect on consumers," Fries said in a "Squawk Box" interview at the World Economic Forum in Davos, Switzerland.

Fries, whose cable and telecommunications company is headquartered in London, said Liberty will continue to develop its fiber-based networks throughout the U.K. but was concerned others may not do the same.

"We're investing £3 billion right now, as we speak," the CEO said. "We're not going to stop, but if other companies that were investing billions of pounds say, 'Well, maybe I'll invest 2 billion instead of 3 billion,' there's a trickle-down effect of that."

Fries spoke a day after British Prime Minister Theresa May detailed how the U.K. will proceed in its split from the EU. He said her speech showed promise.

"The comments yesterday I thought were well received," he said. "Clarity and confidence are her focus, and that's good. Let's see if it happens."