Thames Valley Police issued an alert on Jan 30 alongside a photo of Mr Sturt.
It stated: “Please can you help us find Craig? The 46-year-old is 6ft, slim, with short dark brown hair.
“When he was last seen he was wearing a grey jacket, a top, black jogging bottoms and white trainers.
“Craig was last seen in Reading, but is from Slough and also has links to Heathrow and the Tottenham Court Road in London. If you see Craig, please do not approach him, instead call 999.”
He remains at large and an investigation is ongoing.
The Metropolitan Police, which is now handling the case, said: “Sturt was reported missing to Thames Valley Police on Jan 25.
Security kept under constant review
“On Jan 31 the case was transferred to the MPS and an investigation is now ongoing, led by the Central North Command Unit.”
They added: “We continue to work with all our partners to review and enhance the already robust security measures in place which are kept under constant review by the wider security partnership.”
A spokesman for Heathrow insisted that Mr Sturt, despite not having a passport, would still have gone through security screening.
They said: “All people who go airside are subject to security screening, including the individual involved in this case. We are supporting the authorities with their investigation.”
British Airways said it was also assisting the authorities.
Mr Sturt was charged with obtaining services by deception, being unlawfully airside and boarding an aircraft without permission.
Such breaches were thought to have been impossible because of increased security and technological advances since 9/11.
The Home Office is understood to be looking into the matter, with one source telling The Sun: “This is a major embarrassment for Heathrow and Border Force.
“Officials in the US are furious and demanding to know how this could have happened.”