* 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
By John Geddie
LONDON, Feb 6 (Reuters) - Sterling hit a one-week low against the U.S. dollar on Monday, adding to a near 2 percent fall last week, 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 begins 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, yet 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 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," said Bunning.
"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 to $1.2450 in early trades, its lowest since Jan. 31, before recovering slightly. At 0920GMT, it was down 0.1 percent at $1.2472. It was marginally higher against a broadly weaker euro.
The pound shed 2 percent last weak against the U.S. dollar last week as investors pushed back their expectations for a Bank of England interest rate hike 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 that traders said created more room for those investors to sell the pound going forward. (Reporting by John Geddie; Editing by Andrew Heavens)