The pound gained 0.3 percent in early London trading to $1.3187, its highest since March 28. The British currency had slipped below $1.30 on Friday on growing fears of a no-deal Brexit.
Against the euro, sterling gained 0.1 percent to 85.135 pence, a one-week high.
May said on Tuesday she would seek another Brexit delay to agree an EU divorce deal with Labour, a last-ditch gambit to break an impasse over Britain's departure that has angered many in her party.