While May's announcement by no means lifts the fog of uncertainty over the pound, it offers a glimmer of hope to investors who are worried Britain might crash out of the EU without a withdrawal deal on April. 12.
That helped the currency overlook a downbeat survey of purchasing managers in the services sector, with the headline reading for March dipping into contraction territory to its lowest level since July 2016.
"Expectations of a delayed soft Brexit is buoying the pound but there is a long road ahead," said Lee Hardman, a currency strategist at MUFG in London.
The pound gained 0.3 percent in early London trading to $1.3187, its highest since March 28. The currency had slipped below $1.30 on Friday on fears of a no-deal Brexit.
It is up more than 1.3 percent from Tuesday's low of $1.3015, struck after lawmakers' failure on Monday to agree an alternative plan to May's withdrawal agreement pushed Britain closer to a no-deal Brexit, the worst scenario for sterling.
Against the euro, it held near its strongest level since March. 27 at 85.03 pence.
Expectations for big swings in the pound remained high, with one-month implied volatility holding near three-month highs, contrasting with a similar gauge for the euro, which has plummeted to a 4-1/2 year low.
May will not set preconditions when she begins talks aimed at breaking the Brexit deadlock with opposition Labour leader Jeremy Corbyn on Wednesday, her Brexit minister Stephen Barclay said.
"This (reaching out to Labour) is right and proper and I think a soft Brexit is the right outcome even it will infuriate both wings of the debate," said Chris Bailey, a European strategist at Raymond James in London.