* European shares dip but Britain's FTSE hits record high
* Sterling falls vs dollar and euro after PM May Brexit comments
* Oil falls as Iran exports surge
* Graphic: World FX rates in 2016 http://tmsnrt.rs/2egbfVh
By Nigel Stephenson
LONDON, Jan 9 (Reuters) - The dollar edged higher on Monday, boosted by robust U.S. wage growth data strengthening the case for more Federal Reserve interest rate increases, while Britain's pound fell on Prime Minister Theresa May's hint at no membership of the EU's single market.
Britain's blue-chip FTSE 100 index .FTSE nonetheless hit a record high as the first full trading week of 2017 on London markets began. The pan-European STOXX 600 index .STOXX 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 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 .MIAPJ0000PUS 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 .AXJO rose 0.9 percent while Hong Kong shares .HSI 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 U.S. President-elect Donald Trump may give more details of his policies before his Jan. 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 Nov. 8 election.
The Dow Jones Industrial Average .DJI came within one point of the 20,000 mark for the first time on Friday while the S&P 500 .SPX and Nasdaq .IXIC 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 .DXY , which measures the greenback against a basket of currencies, was just about in positive territory. The euro EUR= rose 0.1 percent to $1.0544 while the yen EUR= fell 0.3 percent to 117.21 per dollar.
Sterling GBP=D4 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 EURGBP= 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. 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.
GERMAN BONDS
German 10-year government bond yields DE10YT=TWEB , the benchmark for euro zone borrowing costs, last stood at 0.29 percent, down 0.5 basis points on the day.
It earlier rose close to 0.33 percent, its highest since Dec. 19, after data showed German exports rose 3.9 percent in November, their strongest monthly gain since May 2012 and far ahead of forecast.
Oil prices fell on a surge in Iranian exports as U.S. producers added more rigs. crude LCOc1 , the international benchmark, last traded at $56.68 a barrel, down 43 cents.
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