* Pound falls 1.3 percent after two of PM May's ministers quit
* Dollar rallies against sterling to 3-1/2 week high
* Yuan records biggest daily rise in more than three months (Updates analyst quote, prices)
By Kate Duguid
NEW YORK, July 9 (Reuters) - The British pound on Monday recorded its largest daily drop against the U.S. dollar in 3-1/2 weeks after two euroskeptic ministers announced their resignation from UK Prime Minister Theresa May's cabinet, leaving the British leader's Brexit plans in chaos.
Foreign Secretary Boris Johnson stepped down on Monday just hours after Brexit minister David Davis's resignation on Sunday evening, calling into question May's ability to deliver the vision of continued close ties with the European Union that she said they had agreed to last week. Davis had been in charge of exit negotiations with the bloc.
The two departures shatter May's own proclamation of cabinet unity last Friday, when she believed she had, after two years of wrangling, secured agreement on Britain's biggest foreign and trading policy shift in almost half a century.
The pound fell 1.3 percent against the dollar to a daily low of $1.319. In mid-afternoon trade, the pound recovered some of those losses, last at $1.326, following the news that UK Conservative Party Chairman Brandon Lewis said he did not expect a vote of confidence against the prime minister.
On the back of sterling's slide, the dollar index rose 0.5 percent against a basket of six major currencies to a daily high of 94.206. Against the euro, the dollar strengthened to $1.173. Analysts attributed the dollar rally to the British currency's move.
"Sterling was very influential. If you actually look at the timeline between Eurodollar's slide and sterling’s slide, the two are very much going hand-in-hand," said Alan Ruskin, global head of currency strategy at Deutsche Bank. "Sterling was driving Eurodollar today."
Other safe-haven currencies also benefited. Against the pound, the Swiss franc strengthened to a daily low of 1.309. The sterling/Japanese yen cross rate also strengthened to a daily low of 146.12.
Investors appear to be ignoring the worsening trade conflict between the United States and China after the two countries imposed tariffs on $34 billion worth of each others' goods on Friday
"There was nothing really surprising" in Friday's trade announcement, said Omer Eisner, chief market analyst at Commonwealth Foreign Exchange Inc. "China’s response was measured and as a result I think we’ve seen the overall risk sentiment in markets improve."
The yuan rose more than half a percent in offshore markets to 6.614 against the dollar, putting it on course for its biggest one-day rise in more than three months and further away from June's lows - its biggest-ever monthly decline.
Reporting by Kate Duguid; Additional reporting by Tommy Wilkes and Saikat Chatterjee; editing by Larry King and Dan Grebler