* 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, Oct 5 (Reuters) - Britain's pound skidded half a percent to three-week lows against the dollar and euro on Thursday, as investors worried about Prime Minister Theresa May's ability to cling onto power after a poorly-received speech the previous day.
May had wanted to use the annual Conservative party conference to pitch herself as the only person able to deliver Brexit, despite interventions by her foreign minister Boris Johnson, and to keep opposition Labour leader Jeremy Corbyn out of power.
Instead, the prime minister's bid to reassert her dwindling authority was marred by a keynote speech that was interrupted by repeated coughing fits, a prankster and even letters of her slogan falling off the stage.
"The speech has been received poorly, which will heighten speculation over a potential leadership challenge in the near term. This additional uncertainty could weigh modestly on the pound," wrote MUFG currency economist Lee Hardman, in London.
Hardman added, though, that economic data suggested growth was solid enough for the Bank of England to raise interest rates at its next policy meeting next month, which would provide support for the pound.
ING currency strategist Viraj Patel said political uncertainty could limit any boost for sterling from a rate hike.
"More confusion over the governments Brexit transition deal strategy...and ongoing questions over Mays leadership... may limit the effects of any BoE policy-driven upside in the near-term," Patel said.
Having reached its highest levels against the dollar since the results of last year's vote for Brexit on expectations that the BoE will indeed move in November, sterling has fallen back more than 3 percent in the last two weeks on worries over a lack of unity in government, and worries about Brexit and its effect on the economy.
On Thursday the pound fell half a percent on the day to $1.3175, the pound's weakest since Sept. 14. It also weakened half a percent to 89.34 pence per euro.
It had been knocked on Wednesday by comments from ratings agency Standard & Poor's, which said it was "a bit sceptical" that Britain's economy needed an interest rate increase soon, and that hawkish comments from the BoE were designed to push up sterling and cool inflation.
"The immediate problem facing (BoE Governor) Carney is that if credibility dictates that the BoE must now raise rates in November, it risks compounding the present slowdown just as the Brexit negotiations reach a critical stage thereby raising the prospect of a reversal of policy at some point," wrote BNY Mellon currency strategists in a note to clients.
Later in the day, BoE Chief Economist Andy Haldane and fellow policymaker Ian McAfferty - who has been voting to raise rates immediately - will be closely watched for clues on monetary policy.
Investors are also watching out for the release of the latest minutes from the European Central Bank. (Reporting by Jemima Kelly; Editing by Toby Chopra)