Home secretary Priti Patel is said to be looking into claims that a passenger arriving at Heathrow airport from South Africa was able to cross the border without facing any COVID checks.
Sharon Feinstein, who lives in Islington, north London, claims she walked through the terminal following a trip to Johannesburg, where the mutant strain is rife.
Although she had received a negative COVID test before departing from South Africa, Feinstein said she was not asked whether she had the virus and was ushered through passport control "within 10 minutes".
Health secretary Matt Hancock told the Commons today that Priti Patel "is looking into this individual case".
Feinstein is now self-isolating at her home and told Good Morning Britain on Tuesday she was left "looking around" for someone to show her test to.
She said: "I was shocked. I fully expected to take around a hour.
"I had my negative COVID test, I had my passenger locator form, I had various other forms.
"We were all queuing up, then I was ushered towards the electronic booth. I was literally through there in 10 minutes.
"Nobody was there. I was looking around for someone to show my test to."
Labour MP Yvette Cooper asked Hancock about Weinstein's claims in the House of Commons this morning.
The chairwoman of the Commons Home Affairs Select Committee said: "Yesterday the Home Secretary told me in Parliament that 100% compliance checks were now taking place at the border.
"Yet one passenger arriving at Heathrow yesterday from South Africa via Qatar has reported having no checks on her forms or tests and being sent on her way through passport e-gates."
Responding, Hancock told the Commons: “The Home Secretary is looking into this individual case and the measures that we announced today further strengthen the enforcement to make sure that the rules that are currently in place are enforced more strongly and indeed that we have brought in a new system of rules to strengthen the safeguards at our border yet further.”
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It comes as the government announced on Tuesday that international travellers who break COVID rules will be subject to draconian new fines.
Arriving travellers will be put in quarantine hotels in England and charged £1,750 for their stay, Hancock said.
Passengers also face fines of up to £10,000 for failing to quarantine and those who lie on their passenger locator forms face up to 10 years in jail.
The cabinet minister told the Commons that 16 hotels have been contracted for the hotel quarantine programme which begins on Monday.
Hancock told the Commons: "People who flout these rules are putting us all at risk.
"Passenger carriers will have a duty in law to make sure that passengers have signed up for these new arrangements before they travel, and will be fined if they don't, and we will be putting in place tough fines for people who don't comply.
"This includes a £1,000 penalty for any international arrival who fails to take a mandatory test, a £2,000 penalty for any international arrival who fails to take the second mandatory test, as well as automatically extending their quarantine period to 14 days, and a £5,000 fixed penalty notice - rising to £10,000 - for arrivals who fail to quarantine in a designated hotel."
He added: "I make no apologies for the strength of these measures, because we're dealing with one of the strongest threats to our public health that we've faced as a nation."