Britain's blue-chip FTSE 100 index nonetheless hit a record high as the first full trading week of 2017 on London markets began. The pan-European STOXX 600 index dropped 0.4 percent in early deals.
Britain's pound was the big mover on currency markets, falling against the dollar and the euro, in reaction to weekend comments from Theresa May that were interpreted as suggesting the country could face a "hard Brexit" without access to the single market when it leaves the European Union.
"The rise in the FTSE is really down to the weakness in sterling, but the Brexit news is not great so I don't see the FTSE gaining too much," said Ipek Ozkardeskaya, market strategist at London Capital Group.
In Asia, MSCI's ex-Japan Asia-Pacific shares index was flat on the day, having risen as much as 0.5 percent after posting a rare loss in the previous session. Australia's S&P/ASX200 rose 0.9 percent while Hong Kong shares rose 0.2 percent.
Trading was light because Japan is shut for a holiday.
A focus for the week will be a news conference on Wednesday at which President-elect Donald Trump may give more details of his policies before his January 20 inauguration.
Expectations of more economic stimulus from a Trump administration have helped push U.S, stocks and bond yields higher since his victory in the November 8 election.
The Dow Jones Industrial Average came within one point of the 20,000 mark for the first time on Friday while the S&P 500 and Nasdaq hit record highs.
Friday's closely-watched U.S. employment report showed fewer jobs than forecast were created last month, although a rebound in wages indicated economic strength and set the stage for more Fed hikes later in the year.
The dollar index, which measures the greenback against a basket of currencies, was just about in positive territory. The euro rose 0.1 percent to $1.0544 while the yen fell 0.3 percent to 117.21 per dollar.
Sterling fell 0.9 percent to 1.2172, having touched it slowest since late October at $1.2163, and dropped more than 1 percent against the euro to an eight-week low of 85.65 pence.
This followed comments from May that she was not interested in keeping "bits of membership" of the European Union when the country leaves the bloc.
"Since October it's become clear that sterling has a very binary relationship with political news, and anything which suggests a 'hard Brexit' sends sterling down, and anything that suggests a 'soft Brexit' sends sterling up. That's been the case since the party conference in October," said Rabobank currency strategist Jane Foley.