After a day of high drama in Westminster, lawmakers voted to take control of parliamentary business that will allow them to push through a bill preventing a no-deal Brexit.
The move was a slap in the face for new Prime Minister Boris Johnson, with several members of his own Conservative party voting against him and defying a warning of an election in mid-October.
Sterling at one point plunged to $1.1959 on Tuesday -- its weakest level since 1985 except for a 2016 "flash crash" -- but rebounded as traders bet Johnson's loss would take a no-deal divorce off the table. Most economists say such a scenario would hammer the British economy.
Still, the development means a continued period of uncertainty for the country.
Wednesday's "session of parliament promises more viewing pleasure, with the possibility that the UK will be heading to the polls... one of the many possible permutations. This story is one that will just keep on giving as the week progresses", said Jeffrey Halley, senior market analyst for Asia-Pacific at OANDA.
Most Asian equity markets rose after two days of stuttering, with Trump's fresh warnings to Beijing over the trade stand-off having little impact.
The president threatened China that if it did not move quicker in negotiations it would get a worse trade deal from him if he won the next election in 2020.
"While I am sure they would love to be dealing with a new administration... 16 months PLUS is a long time to be hemorrhaging jobs and companies," Trump said in a tweet.
"And then, think what happens to China when I win. Deal would get MUCH TOUGHER!"
- 'Significant air pocket' -
The outburst comes as reports said the two sides were struggling to agree parameters for the next round of talks, which Trump had said would go ahead this month.
Beijing's point man in the talks, Vice Premier Liu He, met two Republican senators Steve Daines and David Perdue on Tuesday in the Chinese capital and said he wanted a negotiated resolution based on "equality and mutual respect", state news agency Xinhua reported.
In early trade, Hong Kong rose 1.5 percent, Shanghai, Singapore and Seoul each gained 0.4 percent and Taipei put on 0.7 percent.
But Sydney fell 0.7 percent after data showed the Australian economy expanded at its slowest annual pace for 10 years.
The broad gains also came despite a shock drop in US factory activity into contraction -- the first time since Trump came to power and raising concerns about the state of the world's top economy.
The figures come days before the release of the closely watched jobs data on Friday, which is pored over for an idea about the Federal Reserve's plans for monetary policy with observers tipping it to cut interest rates again at some point.
"The US economy just hit a significant air pocket and just like in an aeroplane experiencing a rapid drop, it's not a question about stabilisation but rather how long and how intense the fall will be," said Stephen Innes, Asia-Pacific market strategist at AxiTrader.
"With the US manufacturing index unceremoniously plummeting into contraction, there is some thought this could force the Federal Reserve to pull multiple rate cut levers this month, which could be viewed as incredibly supportive for risk assets."