Sterling was last up 0.2% against the dollar at $1.2467 and flat against the euro at 85.90 pence, close to its strongest in six months.
The pound fell by 1% against the dollar in May, its largest monthly slide since February's 2.8% loss, but it's still up 3.1% so far in 2023.
Against the euro, sterling gained 2% last month - the most in a month since last July.
UK inflation fell to 8.7% in April from a peak of 11.1% in October, while U.S. inflation is down to 4.9%, from 9.1% last June - when UK inflation was at 9.4%.
The Fed, meanwhile, took just seven months from that time to raise rates by the same amount and U.S. rates are at 5.25%.
Persons:
BoE, Sterling, it's, Stephen Gallo, BoE policymaker Catherine Mann, Mann, Amanda Cooper, Mark Potter
Organizations:
Federal Reserve, Bank of England, Nationwide, BMO, Pictet, Thomson
Locations:
Britain, United States, U.S, Swiss