The Islamic State (ISIS) mastermind of the Paris terror attacks in November last year that killed 130 people had entered the UK by ferry just months before, according to a media report.
Abdelhamid Abaaoud was a wanted terrorist at the time when he managed to travel undetected through a port in Kent, believed to be Dover on the southeast coast of England, The Guardian reported.
The UK Home Office is facing calls to launch an urgent review of security at the country's ferry terminals.
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Burnham added: "Not only did we discover last week that a UK terror suspect on bail waltzed out at the border, we now learn a terror suspect from the continent freely walked in through the same route.
"It would appear extremists perceive the ferry border to be a weak link. The home secretary must conduct an urgent review of border security at ferry terminals and provide urgent reassurance that passports are being properly checked on exit and arrival in the UK."
Counter-terrorism officials are still assessing whether the purpose of Abaaoud's trip to the UK was to plan an atrocity in Britain.
Keith Vaz, the Indian-origin MP who chairs the influential parliamentary home affairs committee, told The Guardian that the government had vital questions to answer: "It is remarkable that this terrorist entered and exited the country.
"He must have been on a watch list. Serious questions need to be answered so that we can prevent a repetition of what actually happened."
Abaaoud, a 27-year-old Moroccon-born Belgian national, was killed in a shootout with French security forces days after he led the Paris attacks and months after he had been in Britain, the report said. He was the head of an ISIS unit set up to send European-origin extremists back to their home countries to carry out terrorist attacks.
Burnham had yesterday challenged UK home secretary Theresa May in Parliament on the issue of terror suspects moving freely across Europe, but she reiterated her refusal to comment on individual cases which relate to police investigations.
She said: "I said to you and indeed others last week, and I will say again today, that I am not going to comment on individual cases because of issues relating to police investigations and proceedings that take place.
"But what I would say is that it is this government that has taken significant steps to enhance our border security, including in establishing the UK Border Force, taking it out of the failed UK Borders Agency which was set up by the last Labour government.