Jeremy Hunt has said the Government must introduce quarantine hotels for international arrivals to combat "massively more dangerous" new coronavirus strains.
The senior Conservative MP joined Labour on Friday in calling for an increased border protection over fears vaccines may be less effective on novel variants.
Ministers are considering forcing new arrivals to the UK to complete their isolation periods in hotels but it is understood no decision to approve the proposal has been made.
Mr Hunt, the chairman of the Health Select Committee, told the Commons: "If we're going to bring down the horrific death rates that we're now seeing, should we not be securing our borders with quarantine hotels, ending household mixing outside bubbles and following Germany in mandating FFP2 masks in shops and on public transport to give better protection to wearers?"
Health Secretary Matt Hancock said he had been advised that the current guidelines on protective equipment were "right and appropriate" and said "very significant measures" were in place for international travel.
"We remain vigilant on what we need to do to guard against new variants coming in from abroad," he added.
"The new variants do change this question because it's not just about ensuring we don't get extra cases coming in from abroad . it's making sure new variants that might not be dealt with as effectively by the vaccine don't arrive and stopping them from coming."
Government sources said no decision on quarantine hotels had been made yet, and expected them to be discussed at a meeting of the Covid-19 committee on Friday or Monday.
Labour leader Sir Keir Starmer said he was not against the idea of hotels being used as quarantine facilities but that the key issue was checks taking place on whether arrivals were abiding by the current quarantine rules.
"The most important thing is not where somebody is located but are we checking, is the system really working, and that's been the structural flaw since the start," he told reporters.
"Wherever people go are they being checked on, that's the critical question. If that works better in hotels then so be it. I don't stand or fall on hotels, I stand or fall on how well the system works."
On Monday, the Government closed the travel corridors scheme that exempted arrivals from having to quarantine if they arrived from countries deemed safe.