Sterling drifted a third of a percent higher on Friday as a generally weak dollar prompted some investors to cut their large bearish bets against the British currency.
Against the dollar, the pound rose 0.33 percent to $1.2692. Versus the euro, the pound was flat at 90.37 pence.
"Sterling is a bit volatile before the Parliament vote next month but there are a lot of cross-currents at play," said Thu Lan Nguyen, an FX strategist at Commerzbank in Frankfurt.
Prime Minister Theresa May's Brexit deal can be passed by the British parliament if the European Union provides clarification that the Northern Irish "backstop" will be temporary, foreign minister Jeremy Hunt said.
Overall short positions against the pound showed another increase, with total bets rising to $4.8 billion in the week ending Dec. 21, according to futures data, after a brief drop earlier this month.
A decline in the number of mortgages approved by British high street banks flattened out last month, with the first year-on-year rise since September 2017, figures from industry group UK Finance showed on Friday.
So far in 2018 sterling has shed around 6 percent as investors worry Britain is headed for a disruptive divorce from its biggest trading partner.
May pulled a vote on her divorce deal earlier this month after admitting that parliament would reject it. Lawmakers are set to discuss the agreement again next month, with a vote in the week starting Jan. 14.
That is keeping currency traders on edge, with implied volatility, a gauge of expected currency swings, rising to a two-week high of 13 percent. The rise in implied options is in contrast to actual moves in the pound.
