Howard Davies, chairman of British bank RBS, told CNBC on Tuesday that the U.K. risks a slowdown to its economy if uncertainty over Brexit continues.

In October, the Royal Bank of Scotland said it had set aside, as an impairment provision, 100 million pounds ($128 million), in order to account for economic uncertainties - Brexit being the biggest concern for the British lender.

"If we get continued political uncertainty for some period, which is now quite possible, then I think we may see a weakening in the U.K. economy," he told CNBC's Joumanna Bercetche at the UBS European Conference.

Davies added that the bank is seeing a slowdown in the pipeline of loan applications for investment as businesses wait on the outcome of Brexit. "If you have a choice to invest or not invest in present circumstances, I think sitting on your hands looks like a prudent strategy."

Davies said the probability of a "no-deal" Brexit, where Britain crashes out of the European Union with no trade agreement in place, had not increased in his view.

But he cautioned, the chances had risen that U.K. leader Theresa May's proposal, known as the "Chequers plan," would likely fail the test of fellow lawmakers. The RBS chairman said a prepackaged deal was starting to look like an option.

"Some kind of continued customs union but nothing special for the U.K., or as people are taling about a potential Norway option," he said.

Davies said Theresa May was sticking fast to her plan as she was likely receiving a lot of advice to say that a no deal Brexit "really could be a mess."

"I'd be very surprised any prime minister, however 'Brexit-enthusiastic' they may be, faced with that advice would say well you know what you can say that, but I'm just going to go for it."