The ongoing Brexit negotiations are still causing anxiety for U.K. firms, with the chief executive of insurer Lloyd's of London telling CNBC that businesses "can't live with this uncertainty."

Inga Beale said Wednesday that her business, one of the world's oldest insurers, had "taken its future into its own hands" and was going to open up a subsidiary in Brussels. She added that around 2 billion euros ($1.76 billion) of the company's business has to go through an EU-based entity and it will lose all of its licensing post-Brexit.

"Other businesses will be doing the same, we can't live with this uncertainty," she told CNBC at the World Economic Forum (WEF) in Davos, Switzerland.

"The uncertainty is really not helping the population at large, and people want to know what's going to happen, but of course we've just started to see the pound start to recover a little bit against the dollar so it looks like there could be a bit of confidence coming back."

The U.K. government and EU negotiators are set to enter a second phase of negotiations centering on a trade deal after a difficult first phase of negotiations focused on the "divorce bill" and how much the U.K. owes the EU before it leaves, the thorny issue of EU and U.K citizens' rights post-Brexit and the border between the Republic of Ireland and Northern Ireland.