(Updates prices, adds sterling, Swedish crown moves)

* Republican healthcare bill collapses in Senate

* Further undermines faith in Trump's ability to legislate

* Dollar hits lowest since September

* Aussie dollar surges 1.8 pct after central bank minutes

* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh

By Patrick Graham

LONDON, July 18 (Reuters) - The U.S. dollar sank to a 10-month low against a basket of major currencies on Tuesday, as the collapse of President Donald Trump's latest healthcare bill eroded confidence in his ability to legislate to boost growth.

The Australian dollar was by far the biggest beneficiary, jumping 1.8 percent to more than two-year highs after minutes from a Reserve Bank policy meeting showed it turning more upbeat on the economy.

In four weeks dominated by doubts over the Federal Reserve's ability to raise interest rates further, and signs that other major central banks are finally turning more hawkish, the dollar is now down more than 3 percent.

At 94.650 on Tuesday, the dollar index was down 8.8 percent from the 14-year peak of 103.82 hit on Jan. 3. The euro rose 0.7 percent to $1.1564, its strongest since May last year.

"Clearly anything that comes along at the moment just corroborates the market's negative attitude to the dollar," said Neil Mellor, senior FX strategist with Bank of New York Mellon in London.

"There's just not enough inflation at the moment. And anything like this (defeat for Trump) is liable to push it lower."

Two more Republican Senators, Jerry Moran and Mike Lee, announced their opposition late on Monday to a revised Republican healthcare bill, leaving efforts to pass the legislation in chaos.

"If the bills won't pass, there will be no money for tax cuts. The implementation of his fiscal policy will be difficult," said Bart Wakabayashi, Tokyo Branch Manager of State Street.

Friday's weak reading on U.S. inflation and retail sales also fanned speculation the Fed may not have justification for another rate hike by the end of this year, despite policymakers' projection for such a move.

Money market instruments price in less than 50 percent chance of a rate increase for the rest of the year.

In contrast, central bank policymakers in the euro zone, Britain and Canada have recently signaled they could adjust their policies, with the Bank of Canada raising rates last week for the first time since 2010.

But the latest signs from New Zealand, Sweden and the United Kingdom all point in the opposite direction.

British inflation surprised by falling for the first time since October, knocking a whole cent off the value of the pound against the dollar and weakening it 1 percent against the euro.

For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Opener=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Additional reporting by Hideyuki Sano in TOKYO; Editing by Raissa Kasolowsky and Mark Potter)