* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1
* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv
LONDON, Nov 13 (Reuters) - Sterling fell against the dollar and euro on Monday as investors worried about Theresa May's ability to stay on as British prime minister and get what they consider to be a good exit deal from the European Union.
May's blueprint for Britain's departure from the EU faces a crucial test starting on Tuesday, when lawmakers try to win concessions on the government's legislation to sever ties.
That test comes after the Sunday Times reported that 40 lawmakers from her ruling Conservative Party had agreed to sign a letter of no-confidence in her - eight short of the number needed to trigger a leadership contest.
It also follows reports over the weekend that the prime minister had been sent a letter from two pro-Brexit members of her cabinet, Boris Johnson and Michael Gove, giving her apparent instructions on how to run Brexit.
Sterling is sensitive to any signs Britain could be heading towards a "hard" Brexit - a scenario in which the country would lose any kind of preferential access to the single markets.
It is also sensitive to domestic political uncertainty, and any risk that another election could be called.
The pound fell as much as 1 percent earlier on Monday to hit a one-week low of $1.3063, before recovering to trade around $1.31 by 1730 GMT, still down 0.7 percent on the day.
"Investors are particularly concerned at this latest suggestion of disunity in the government as it comes days after the latest round of Brexit talks showed little progress," said William Anderson Jones, head of UK corporate dealing at RationalFX, a brokerage.
Against the euro, sterling lost 0.6 percent to trade at 88.98 pence.
Bond yields have in recent days also moved against sterling, eroding a source of support, despite a rate hike by the Bank of England earlier this month.
Differentials between U.S. and British 10-year bond yields have widened to nearly 120 basis points in Treasuries' favour, compared to 96 basis points in mid-September.
But analysts said the main focus for sterling was its political backdrop.
"Once again sterling is carrying the mantle of the worst-performing G10 currency on a one day view and once again politics is behind the pressure on the pound," wrote Rabobank analysts in a note to clients.
"Without a strong leader, investors will fear that the prime minister will be distracted and that the UKs negotiating position (with the EU) will be compromised." (Reporting by Saikat Chatterjee; editing by John Stonestreet; Editing by Toby Chopra)