Mr Bailey said the Bank of England estimates that public sector employment had increased by “200,000 to 300,000” during the pandemic, one of the biggest expansions of the state for generations.
“The shortfall in employment in consumer-facing services industries, which are looking for active labour, is not far off the same number,” he told the Sunday Times.
“So if you think about competition in the labour market, the public sector has increased.”
Official figures show that since the end of 2019, the public sector has gained around 246,000 staff.
This included some 118,000 who joined the NHS, 58,000 who went into public administration, 16,000 who joined the police, 12,000 who went into education and 6,000 recruits for the armed forces.
Another 41,000 went into “other public sector” roles, a classification that includes rail companies which received state bailouts.
At the same time, analysis of vacancy data from the Office for National Statistics suggests there will be 163,000 empty posts in the hospitality sector by the end of December – up from 151,000 vacancies at the end of October.
The forecasts, compiled by hospitality app Stint, suggest more pain is ahead for restaurants, hotels, bars and cafes, which have only just managed to recover to pre-pandemic levels of trading after a series of lockdowns.
Sol Schlagman, co-founder of Stint, said: “The hospitality industry could be facing a second tough Christmas if these staffing holes aren’t plugged in time.”