* 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 (Adds context about Brexit+BOE, new quotes)
LONDON, Oct 9 (Reuters) - Britain's pound rose almost 1 percent on Monday, rebounding from its biggest weekly drop in a year, after British Prime Minister Theresa May said she would resist challenges to her leadership.
May hinted at the weekend that she may be considering a cabinet reshuffle to reassert her authority, raising questions over the fate of foreign minister and Brexit campaigner Boris Johnson, who has been accused of undermining her.
Sterling rose 0.9 percent to $1.3180 -- recovering from the 2.5 percent it lost last week -- and was the biggest gainer among major currencies against a broadly muted dollar.
It also rose 0.8 percent to 89.08 pence per euro.
The pound has become more sensitive to political noise in recent months and some strategists said Johnson's departure, if it happens, could increase the chances of a "soft Brexit", which might be positive for sterling in the short term.
"If Boris Johnson was to leave or be demoted as the weekend press is suggesting, that would be showing May's leadership and that her vision of Brexit is the one that will be going forward and that markets should be aligned to," said Viraj Patel, an FX strategist at ING Bank in London.
Speculative investors, meanwhile, turned more positive on the pound in the week to Oct. 3 than at any time since September 2014, according to data from the Commodity Futures Trading Commission.
Patel said this long positioning was the result of heightened expectations the Bank of England will raise interest rates soon.
May is expected to give British lawmakers a bullish prognosis for negotiations over the exit from the European Union on Monday, but will tell them that it is up to Brussels to make the next move.
But investors remain wary as to whether May will succeed in advancing towards a transition deal.
"The EUs lack of willingness to begin talks over a new special relationship highlights the need for the UK government to prepare more intensively for a no deal scenario even if it is not the desired outcome," warned currency analyst Lee Hardman in a note for MUFG.
Last week's losses had dragged down sterling from a June 2016 high of above $1.3650 hit in late September and erased all its gains sustained after the BoE signalled in mid-September an interest rate increase was likely in the coming months.
On a trade-weighted basis, sterling fell on Friday to its lowest since mid-September.
Adding to sterlings woes have been weak economic data releases pointing to tepid growth in Britains economy.
Figures on Friday showed British economic productivity fell at its joint-fastest annual rate since 2013 in the 12 months after the country voted to leave the European Union.
(Reporting by Fanny Potkin; Editing by Catherine Evans)