* European shares dip but Britain's FTSE hits record high
* Wall Street seen opening lower after Friday's record highs
* Sterling falls vs dollar and euro after PM May's Brexit comments
* Oil falls on signs of U.S. output growing
* Graphic: World FX rates in 2016: tmsnrt.rs/2egbfVh
By Nigel Stephenson
LONDON, Jan 9 (Reuters) - The dollar edged up on Monday, boosted by robust U.S. wage growth data that strengthened the case for more U.S. interest rate rises, while Britain's pound fell on comments by Prime Minister Theresa May seen as pointing to a "hard" Brexit.
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 0.5 percent in early deals.
Wall Street, which hit record highs on Friday, also looked set for a cautious start, with index futures lower as oil prices fell.
Britain's pound was the big mover on currency markets, falling 1 percent against the dollar and the euro, in reaction to weekend comments from May that were interpreted as suggesting that she would prioritise reducing immigration over access to the European Union single market when Britain leaves the EU.
"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 up 0.1 percent, having earlier risen as much as 0.5 percent. Australia's S&P/ASX200 rose 0.9 percent while Hong Kong shares rose 0.2 percent.
Trading was light because Japan was 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 the policies he will seek to implement after he takes office on Jan. 20.
Expectations of more economic stimulus from a Trump administration have helped to boost U.S. stocks and bond yields.
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 that fewer jobs were created last month than forecast, although a rebound in wages pointed to 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, rose 0.1 percent on Monday. The euro weakened marginally to $1.0525 while the yen rose 0.3 percent to 116.64 per dollar.
Sterling fell 0.9 percent to $1.2166, having touched its lowest since late October at $1.2122, and weakened 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 Britain leaves - even though she said on Monday that she had said nothing new in Sunday's interview.
"May saying that it's not about keeping 'bits' of the EU suggests it's not going to be about keeping access to the single market," said HSBC currency strategist Dominic Bunning.
The German 10-year government bond yield, the benchmark for euro zone borrowing costs, last stood at 0.28 percent, down 1.5 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 signs of growing U.S. production outweighing optimism that other producers were sticking to a deal to cut output to bolster prices.
Brent crude, the international benchmark, last traded at $55.96 a barrel, down $1.14 cents or 2 percent.
"We see the optimism surrounding OPEC and non-OPEC production cuts being counterbalanced by fears of higher U.S. crude production as the higher rig count of last Friday still weighs," said Hans van Cleef, senior energy economist at ABN Amro.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Saikat Chatterjee in Hong Kong, Jemima Kelly, Marc Jones, Dhara Ranasinghe and Karolin Schaps in London; Editing by Kevin Liffey