Johnson said Britain would not adhere to EU rules and regulations, sending sterling to a six-week low on Tuesday. It rebounded after a better-than-expected construction survey.
Traders will be watching the final reading of the UK services purchasing managers' index, which economists polled by Reuters expected would remain at 52.9 in January.
The pound was up 0.1pc at $1.3043 and 0.2pc higher versus the euro at 84.61 pence.