Video report by Lisa Adlam
Simon Walls, who is the clinical leader of St Cecilia's care home, told ITV News that people's reasons for not wanting to have the vaccine had to be taken into account, but that he understood why relatives would want all staff to be vaccinated.
Mr Walls said: "I imagine there are family members who would say I wouldn't send my relative to a care home unless everyone is vaccinated against the virus, but if you look at something like the flu virus, not everyone [in social care] gets the flu vaccine.
"So it's another one a bit like that because the chances of getting flu and that leading to the death of a resident is another thing you have to bring forward.
"I do understand it from both sides, but this may put off a lot of staff, who are already very difficult to get to come into social care, to come to work."
There has been a broadly high uptake of the vaccine by care home workers in the Calendar region, according to data released by NHS England.
Health Secretary Matt Hancock said: "Vaccines save lives and while staff and residents in care homes have been prioritised and the majority are now vaccinated we need to do everything we can to keep reducing the risk.
"Through our consultation, we have listened to the experiences and concerns of providers and people living and working in care homes to help shape our approach.
"We have a responsibility to do all we can to safeguard those receiving care including in the NHS and so will be consulting further on whether to extend to other health and social care workers.
"This is the right thing to do and a vitally important step to continue protecting care homes now and in the future. I’d urge anyone working in care homes to get their jab as soon as possible."
People coming into care homes to do work will also have to have had two jabs, although visiting family and friends won't have to.
Mike Padgham, who is the chair of the Independent Care Group which represents care homes in Yorkshire, said that he didn't like the idea and that people who have worked hard on the front line for the last 15 months shouldn't face the prospect of dismissal.
"We live in a free country and people should have a choice about what they inject into their body," he said.
"It's one thing recruiting staff and telling them from the beginning they have to be vaccinated, but it's another thing telling people already working for you they have to have it."
He added that he supported the vaccine and believed it was the best way out of the pandemic and he would encourage everyone to have it.
Gavin Edwards, Unison's Senior National Officer for Social Care, said that "coercing" people into having the vaccine was not the way forward and that the government should be encouraging vaccine uptake by making sure care workers get time off to have the jab.
However, the head of the Lincolnshire care group said that she thought a fully vaccinated workforce would be more attractive to new starters.
Gaynor Saunders, Chair of the Hull and East Riding Care Association, said: "With regards to mandatory vaccination of all care home staff, as a provider of care to support the most vulnerable in our society, I advocate any measures that protect those people; many of whom fought and/or contributed in the Second World War for our freedom.
We should be very proud of our vaccination programme, the efficacy and speed at which the rollout was undertaken. However, the science does not yet identify any long term effects of the vaccine in those younger people who make up the largest part of our dwindling workforce.
"It is common knowledge that the sector is in crisis; not least, as a result of a diminishing workforce and I am extremely concerned at how such a decision will further impact our sector."
She added that there should be a longer period for employees to make the decision to have the vaccine.