The pound has risen 0.35% against the dollar to $1.3067 after the Bank of England's Monetary Policy Committee voted to hold the interest rate.
Sterling also gained against the euro, up 0.21% at €1.1849.
The MPC made clear, however, that it may act if the UK economy fails to gain momentum.
"With Mark Carney seemingly having deferred this policy decision to his successor, Andrew Bailey will need to land on his feet running," says Principal Global Investors' market strategist, Seema Shah.
"Unless economic activity data improves measurably over the coming months, reflecting proof of the so-called 'Boris bounce', and interest rate cut is likely to remain on the agenda for 2020.".