The pound rose to $1.4117 versus the dollar, its highest level since April 2018.
Versus the euro, it edged 0.3% higher at 86.17 pence, its highest since March 2020.
The pound has strengthened more than 3% in February against the dollar as traders expect Britain's speedy vaccine roll-out will help the economy rebound from its biggest contraction in 300 years.
Sterling above 1.41 vs dollar 
Johnson set out a phased plan on Monday to end England's COVID-19 lockdown, with schools returning on March 8, when minimal socialising outdoors would also be allowed.
The so-called roadmap would then pass through four stages, with the final step, when most restrictions would be lifted, not starting until June 21 at the earliest.
"Sterling continues to trade firm on the vaccine label and associated easing of lockdown expectations opening the doors to recovery," said Neil Jones, head of FX Sales at Mizuho Bank.
"My sense is the stage is set for $1.45."
Sunak said he would set out more details of job support measures in his budget next week, after official figures showed unemployment had risen to its highest since early 2016.
"The extended roadmap puts increased pressure upon the chancellor into next week's budget, employment support will surely have to extend beyond the current April end date," said Jeremy Stretch, head of G10 FX Strategy at CIBC Capital Markets.
Stretch said that even if at this point sterling looks increasingly overbought, it could rise to $1.4145-$1.4155.
In the meantime, Britons rushed to book foreign holidays after the announcement of the plan to ease the lockdown.
Data showed that almost a million people born outside Britain may have left the country last year in the biggest net outflow of foreign workers on record.
(Editing by William Maclean, Alison Williams and Giles Elgood)
By Joice Alves
