It may be legal for companies to insist on new staff being vaccinated as a condition of their employment, the justice secretary has said.
However, Robert Buckland said it was unlikely bosses could make existing workers have vaccines under their current contracts.
Downing Street has said it would be "discriminatory" to order people to be vaccinated to keep their job.
But some firms say they will not hire new staff who refuse to have the jab.
In an interview with ITV on Wednesday, Mr Buckland said compelling new staff to be inoculated could, in theory, be possible if it was written into their contracts.
However, employers would probably need to take legal action if existing staff refused such an order, he said.
"I think that has to be the case because we're dealing with existing terms of contracts of employment, thousands of existing contracts,” he said.
He added that the legality of “no jab, no job” would depend “very much on the terms of employment and the particular contract”.
"Generally speaking I'd be surprised if there were contracts of employment existing now that did make that approach lawful. I think frankly the issue would have to be tested.”
London-based Pimlico Plumbers is one company that has said it will not hire new staff who have refused the vaccination on non-medical grounds.
Employment lawyers initially questioned the move, but on Wednesday founder Charlie Mullins said he had been advised it was legal.
"We've obviously been talking to lawyers and they're very happy that we can add this proposal to any new workers that start with us once the vaccine is rolled out," he told BBC Radio 4's Today programme.
"We'll be using the new contracts two to three months from now. When people come along for a job with us, if they're not happy to sign that, then again that's their choice, but they certainly won't be given a job with Pimlico Plumbers."
Care home operator Barchester Healthcare has also said all new hires will be obliged to get the jab.
"With regards to our staff, we are doing all we can to reassure and encourage those who are a little more reticent to have the vaccination, and we are also ensuring that all new staff must have the vaccination (if they medically can) before starting work looking after our vulnerable residents and patients who are in our care," Barchester Healthcare wrote on its website.
'Open to challenge'
David Samuels, legal director at law firm Lewis Silkin, said that there is nothing legally to stop a business from placing a "no jab, no job" clause in contracts for new hires.
However, he cautioned that employers would need to analyse each job role and evaluate health and safety risks before introducing such a clause.
Failure to do so would make it possible to challenge a contract as being unfair or discriminatory, if a claimant can prove they are exempt from having the vaccine for some reason, or unable to access it.
There are concerns, for example, that "no jab, no job" policies would disproportionately affect young people who are last in line to get the jab.
"It's going to be harder to justify - especially if they don't go through that process and document it, and it will be more likely that they will be challenged successfully through a legal claim," Mr Samuels told the BBC.
He added that his firm had received enquiries about whether such a clause could be put in place if the business necessitated some staff to work in the office or in a factory.
The prime minister's official spokesman has said: "Taking a vaccine is not mandatory and it would be discriminatory to force somebody to take one."