Stock markets meanwhile rallied, with investors looking past a downgrade of US growth to focus on the next round of top-level China-US trade talks.
Around 1200 GMT, the pound was up 0.4 percent at $1.3100, while the euro dropped 0.3 percent to 85.75 pence.
"Despite plenty of evidence to suggest otherwise, the pound appeared to take an optimistic view ahead of Friday's latest Brexit vote," said Connor Campbell, analyst at Spreadex trading group.
"Having opened the session in the red, sterling may be banking on the likely third failure of (Prime Minister) Theresa May's withdrawal agreement leading to a substantial delay rather than a no-deal exit."
MPs are set for a momentous vote that could end a months-long crisis or risk Britain crashing out of the EU in two weeks.
The House of Commons has twice rejected May's withdrawal agreement, both times by large margins, but has been unable to agree any alternative -- and time is running out.
The pivotal vote takes place on the day Britain was supposed to leave the European Union until May asked the bloc's leaders last week for a little more time.
"Today is going to be another one of those days when traders are going to make decisions mostly based on rumours and this is going to bring crazy moves in sterling," ThinkMarkets analyst Naeem Aslam told AFP.
In equities trading, while the past five days have been dogged by fears over the outlook for the economy, markets have enjoyed a stellar first-quarter overall, mostly on hopes of a US-China tariffs deal and prospect of lower borrowing costs.
In commodities, oil prices were headed for a strong finish to the week, having enjoyed their strongest quarter in 14 years, with Brent crude jumping 26 percent and WTI by 29 percent since the start of the year on tighter supplies.
US President Donald Trump on Thursday called on OPEC to boost oil output following the strong price rises since the beginning of 2019.
The Organization of Petroleum Exporting Countries in December reached a deal to with Russia and some other non-cartel producers to limit output to shore up prices.
"While OPEC, and above all (kingpin member) Saudi Arabia, appeared in November to be obeying US President Trump's repeated demands to increase oil production, his tweets now are more likely to fall on deaf ears," analysts at Commerzbank said Friday.
Oil futures have won support also from unrest in OPEC-member Venezuela.
"US sanctions, power outages and mismanagement are having a massive effect on Venezuela's oil production and oil exports at present," they added in a research note.