Japan's Nikkei 225 fell nearly 1 percent to 21,290.24 while the Topix index was down 0.84 percent at 1,592.07. The Kospi index in South Korea retraced some of its earlier losses and declined 0.41 percent to 2,148.41 while Hong Kong's Hang Seng index slipped 0.52 percent.
Mainland Chinese shares were also lower. The Shanghai composite was down 1.09 percent at 3,026.95 while the Shenzhen composite fell 2.31 percent.
In Australia, the ASX 200 dropped 0.22 percent to 6,161.20 as some of the sectors turned positive before market close. The energy sector fell 0.88 percent as oil stocks struggled for gains.
That was despite a small uptick in overnight oil prices after a Saudi official said the kingdom plans to cut its crude oil exports in April to below 7 million barrels per day as it seeks to drain a global supply glut.
Oil prices continued their upward trend on Wednesday during Asian hours. U.S. crude rose 0.7 percent to $57.27 a barrel while international benchmark Brent was up 0.46 percent at $66.98 at 3:29 p.m. HK/SIN.
Consumer sentiment in Australia deteriorated in March, falling to its lowest level since September 2017, according to a report issued by Westpac Bank and the Melbourne Institute. Respondents were said to have been reacting to a slowdown in Australian economic growth in the second half of last year.
While the route forward appears uncertain, May has already promised two more votes this week for lawmakers to decide if the U.K. should leave the 28-member bloc with no deal, or request a delay to its departure — which is currently scheduled for Mar. 29.
The British pound tumbled from levels above $1.32 to an earlier low of $1.3057. At 2:36 p.m. HK/SIN, sterling traded at $1.3091.
"Tomorrow the House will vote on whether to leave the European Union without any agreement," Joseph Capurso, senior currency strategist at the Commonwealth Bank of Australia, wrote in a Wednesday morning note.
He said that if lawmakers voted to leave without a deal, which is commonly referred to as a hard Brexit, the pound could fall 4 to 8 percent. "It is important to note a majority of MP's are against a hard Brexit," Capurso added.
Other currency strategists urged investors to stay defensive on the British pound.
Philip Wee, a foreign exchange strategist at Singapore's DBS Group, said in a note that there is no guarantee the European Union would accept a possible request from the U.K. to delay its departure unless British lawmakers "demonstrate that they know what they want."
"The surest way to avoid a disorderly Brexit would be to withdraw Article 50 which is potentially another divisive issue," Wee said, referring to the process of leaving the EU. "Having fallen from 1.33 to 1.31 in the past 1-2 weeks, (the pound) could well fall below 1.30 again."
The dollar index, which measures the greenback against a basket of its peers, traded at 96.999, after dropping from levels above 97.200 in the previous week.
Elsewhere, the , considered a safe haven currency, traded at 111.30 to the dollar after strengthening from levels near 111.60 last week.