* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
* British parliament approves Brexit deal, but rejects timetable
* Traders search for positives amid Brexit chaos
* Currencies look for clues on U.S.-China trade war
By Stanley White
TOKYO, Oct 23 (Reuters) - The pound edged lower on Wednesday after an overnight fall as Brexit hung in the balance, with the British Parliament still divided on how, when or even if to engineer Britain's departure from the European Union.
The yen rose against the U.S. dollar and the Australian dollar as some investors sought a safe haven amid doubts about Brexit and efforts to de-escalate a bruising trade war between the United States and China.
A decline in equities and a rise in U.S. Treasury prices in Asia underscored investors' aversion to taking on big risks as the drama over Britain's departure from the EU grows increasingly complex by the day.
On Tuesday, British lawmakers voted by 329 to 299 in favour of Prime Minister Boris Johnson's Brexit plan, but then opposed Johnson's extremely tight timetable to complete the legislative process in three days by 322 to 308 votes.
It is now up to the EU to decide whether to extend Britain's Oct. 31 deadline for its departure from the bloc, although there is hope Britain can avoid the worst case scenario of leaving the EU without any deal in place.
With no major economic data scheduled in Asia on Wednesday, traders will be left to ponder whether Britain will hold a general election to break the impasse.
Investors are also closely watching for signs of a thaw in the U.S.-China trade war, which has cast a shadow over financial markets and global economic growth.
"The pound will adjust in a narrow range for the time being," said Junichi Ishikawa, senior foreign exchange strategist at IG Securities in Tokyo.
"For now, the risk of a no-deal Brexit has receded, but there are still political uncertainties."
The pound fell 0.16% to $1.2856 after a 0.7% drop on Tuesday.
Against the euro, the pound eased to 86.55 pence following a 0.5% decline in the previous session.
Sterling initially rose on Tuesday after parliament approved a second reading of the Brexit deal, but then fell after lawmakers rejected the timetable.
It was the first time parliament has signalled support for a deal on how Britain would leave the EU, but Johnson had warned prior to the votes that he would push for an election if his timetable for Brexit were defeated.
The dollar index against a basket of six major currencies stood at 97.545, holding on to a 0.2% gain posted on Tuesday.
The U.S. currency fell 0.15% to 108.32 yen. The Australian dollar, whose fortunes are closely tied to global trade and commodity prices, gave up 0.32% to 74.16 yen.
In the onshore market, the yuan traded at 7.0842 per U.S. dollar, weaker than its previous close of 7.0778. In the offshore market, it eased slightly to 7.0841.
Treasury prices rose in Asia as some investors sought safe havens, which pushed the yield on benchmark 10-year Treasury notes down to 1.7519% and weighed on the dollar-yen cross.
The United States and China are trying to finalise the first phase of a trade agreement before an Asia-Pacific Economic Cooperation summit in Chile in mid-November.
An exclusive Reuters report that one of the U.S. advisors to U.S. President Donald Trump on trade talks with China will leave government could introduce some uncertainty about future trade talks. (Reporting by Stanley White; Editing by Richard Pullin & Shri Navaratnam)