While the British currency had steadied above $1.28 levels since last week as markets ratcheted up expectations that Britain would not leave the European Union without a deal, market watchers warned of more volatility ahead.
In an outlook note, UBS Wealth Management said Brexit risks make hedging pound exposure preferable over the next three months to avoid volatility and advised against buying sterling at current levels.
While the pound has recovered nearly 4 percent from early January lows to above $1.2850 levels against the dollar, it still remained about 10 percent below from the 2018, highs of above $1.43.
"The risk of more drama that ultimately appears to be going nowhere quickly keeps officials preparing for a no-deal exit," said Marc Chandler, chief market strategist at Bannockburn global forex who expected sterling to be supported in a $1.2800-$1.2825 band.
With around two months to go until Britain is due to leave on March 29, investors advised caution around current levels as there was no sign on how it will leave the world's biggest trading bloc, with the pound trading roughly midway of a two-year trading range.
"Investors have priced out the most negative of scenarios which is a no-deal Brexit but markets need to see more concrete gains before pushing the pound higher from current levels," said Ricardo Evangelista, a senior analyst at ActivTrades Plc in London.
Sterling rose about 0.3 percent from the session lows to trade virtually flat at $1.2868. Against the euro , it was down 0.1 percent to 88.33 pence.
May will make a statement in parliament at about 1530 GMT and put forward a motion in parliament on her proposed next steps on Brexit, though some lawmakers are planning to wrest control of Britain's exit from the government.
Last week, May's deal suffered a heavy defeat in parliament but she won a subsequent vote of confidence.
In a sign of how bullish market participants have become on the prospects of Britain avoiding a no-deal Brexit, one month implied volatility on the pound or expected price swings have fallen to a one-month low below 11 vol.