Mr Bailey said that businesses are "adjusting employment" and offering lower pay rises due to Chancellor Rachel Reeves' increase in national insurance contributions for employers.
He believes the British economy is growing below its potential, which could create "slack" to reduce inflation.
The Governor expressed confidence that the Bank's base rate, currently 4.25 per cent, is on a "downward" path, with the next review scheduled for 7 August.
The government is under pressure to improve living standards, with some Labour figures suggesting a wealth tax, although other tax rises at the autumn budget have not been ruled out.