* Graphic: sterling and gilt yields bit.ly/2dgAXn1
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv (Updates prices, adds quote)
By John Geddie
LONDON, Feb 6 (Reuters) - Sterling hit a one-week low against the dollar on Monday as Prime Minister Theresa May faced challenges over her legislative plan for taking Britain out of the European Union.
A three-day debate on a law giving May the right to trigger Brexit began on Monday and will be followed by a series of votes on whether to attach extra conditions to her plan to start talks by March 31.
Lawmakers voted overwhelmingly in favour of the principle of the new law last week, but Sunday brought the first signs of internal Conservative Party dissent which could see the bill amended, damaging May's authority domestically and potentially giving EU negotiators a powerful lever in the exit talks.
May warned lawmakers not to obstruct the will of voters with a series of amendments of the Brexit legislation. Her spokeswoman said the government would not allow attempts to keep Britain in the EU.
May has said parliament will be given a choice between accepting the deal she has reached with the EU or rejecting it and leaving the bloc without any agreement on issues such as trade and immigration. MPs want to be given more influence.
Dominic Bunning, a currency strategist at HSBC, said the debate raised the risk of a more chaotic outcome which may deter foreign investors that Britain relies on to fund a big deficit in its balance of payments.
"Any signs of a more chaotic outcome, any signs of a more difficult discussion phase will create downward pressure on sterling," Bunning said.
"As soon as you get that uncertainty increasing in the UK, it makes it harder for foreign investors to want to finance the current account deficit."
Sterling fell as low as $1.2427, its weakest since Jan. 31, before recovering slightly. In late trade, it stood at $1.2448, down 0.2 percent on the day.
The pound edged up 0.1 percent against a broadly weaker euro .
"The pound is fairly directionless ... there is no strong trend and it's consolidating at these lower levels," said MUFG analyst Lee Hardman.
The pound shed 2 percent last weak against the dollar as investors pushed back their expectations for a Bank of England interest rate increase and after disappointing services sector data.
Some traders said the market has also been driven recently by shifts in positioning.
Shorts on sterling last week fell to their lowest levels in 2017, a move traders said created more room for those investors to sell the pound.
Reporting by John Geddie/Nigel Stephenson; Editing byLarry King