* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Updates prices)
LONDON, May 17 (Reuters) - Sterling dived to a four-month low on Friday after cross-party Brexit talks collapsed and concern grew about the impact Prime Minister Theresa May's likely resignation would have on Britain's EU divorce.
The pound has traded in a narrow range of $1.29-1.32 since Brexit was delayed in late March, but following weeks of talks between May's Conservatives and the opposition Labour Party that yielded nothing the currency slumped out of its narrow range.
May has agreed to set out a timetable for her departure in early June when parliamentarians are likely to again vote against her thrice-rejected EU withdrawal agreement. .
That raises the prospect of a Conservative leadership battle producing a more Eurosceptic British leader who could move Britain towards a no-deal Brexit, the worst case scenario for sterling.
"What we're seeing is the market pricing in a higher probability of an exit without a deal," Adam Cole, chief currency strategist at RBC Capital Markets, said, noting the growing risk that the bill would fail to pass and May would depart before parliament goes into recess in late July.
"It looks increasingly likely she will be replaced by a pro-Brexit PM with no election, and that automatically increases the chances of a no-deal Brexit."
Sterling was down for a tenth consecutive session, touching a four-month low of $1.2733 and falling 0.6% against the euro to 87.61 pence, the lowest since February 15 .
It is now set for its worst week since February 2018, and a further fall would make it one of the worst weeks in well over a year.
Another outcome could be no Brexit at all -- a boon for the pound -- or the possibility of a general election and a Labour government in power.
"The market doesn't like elections at the best of times, and given it has a natural capitalist orientation, it's not a surprise it worries over this (possible) Labour government," said Neil Mellor, senior currency strategist at BNY Mellon.
On Thursday, the head of Britain's National Grid criticized Labour's plans to re-nationalize energy networks, saying that would increase costs for consumers and might prompt legal challenges.
Next week's European parliamentary vote is another cause for concern, with Nigel Farage's Brexit Party on course to pick up 34% of the vote, more than the Conservative and Labour parties combined.
(Reporting by Abhinav Ramnarayan, editing by Gareth Jones)