(Updates prices, adds quote after start of European trade)

* Republican healthcare bill collapses in Senate

* Further undermines faith in Trump's ability to legislate

* Dollar hits lowest since September

* Aussie dollar surges 1.5 percent 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, hit by the latest collapse of President Donald Trump's efforts to deliver a new healthcare bill in a market deeply worried by the pace of U.S. growth.

The Australian dollar was by far the biggest beneficiary of another slide for the greenback, jumping 1.5 percent to more than two-year highs after minutes from the Reserve Bank's last policy meeting showed it turning more upbeat on the economy.

In four weeks dominated by expectations that 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.

Since hitting a 14-year peak of 103.82 on Jan. 3, at 94.830 on Tuesday, the dollar index was down 8.8 percent.

"Clearly anything that comes along at the moment just corroborates the market's negative attitude o 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 that 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, the UK and Canada have recently signal led they could adjust their policies, with the Bank of Canada raising rates last week for the first time since 2010.

"A lot of countries are catching up with the U.S. in terms of tightening in monetary policy. So it is natural that the dollar is losing its advantage," said Yuki Ishizuki, senior currency strategist at Damian Securities.