The Government has already made jabs compulsory for those working in care homes, with rules taking effect next week.
Last month, watchdogs raised concern that the requirement could worsen the “fragility” of the sector, with low-paid workers instead choosing jobs in hospitality and travel.
Mr Hopson said NHS workers were already being drafted in to cover short-staffing in social care. If compulsory jabs are brought in for the NHS, he said, the service should be given the same five-month notice given to the social care sector – which was warned in June that the rules would take effect this month.
“You just need to look at the problems that social care providers are currently reporting and saying: ‘Look, we are really, really struggling at the moment in terms of staff potentially leaving just at the point when we need them,’” he said.
“And indeed some NHS staff are now having to help out, for example in Cornwall, in the social care sector to ensure that we can discharge people from hospital.”
More time would allow trust leaders to have “supportive, encouraging conversations” with reluctant staff, with take-up lower in groups including women considering starting a family and NHS workers from black communities, he said.
“One of the things we’re saying today is please can we ensure that we don’t have too quick a deadline so that we can carry on that process and, crucially, we can get through winter,” Mr Hopson added.
A Department of Health spokesman said: “We have taken action to introduce vaccination requirements in care homes and we recently consulted on extending this further across health and other social care services. We will set out our response in due course.”