Student nurse Owami Davies was captured on CCTV in the company of a man on the night she was last seen alive.
The Metropolitan Police says the footage shows them crossing Derby Road in West Croydon, south London, just after midnight on 7 July.
Three men have been arrested on suspicion of the 24-year-old's murder.
Her mum Nicol said: "This is such a terrible time for all those who love Owami and I am pleading for anyone who can help find her to contact police."
Two men, aged 23 and 27, were arrested on Monday and a third man, aged 32, was arrested on Tuesday.
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Police said Owami Davies was with a man as she crossed Derby Road on the last night she was seen alive
A property on Derby Road has been cordoned off, as police spent much of Wednesday searching it.
Nicol Davies said: "There are many friends and family who love and care for Owami and all of them want to see her safe return.
"Every day we hope to hear the news that Owami is coming back to us; your help might make it so."
In particular, officers are keen to speak to the driver of a white van that was parked in Derby Road.
Police said Ms Davies and the man she was with crossed the street "just as the van pulled out".
"The van driver would have had a good opportunity to see them both clearly and officers are appealing this possible witness to come forward," a statement said.
Ms Davies was first reported missing by Essex Police on 11 July. The force said she had left the family home in Chafford Hundred, Grays, on 4 July.
In an updated statement on 16 July, the force said Ms Davies was last seen in Croydon on 6 July.
She was wearing a black jumper, grey jogging bottoms and a grey cap.
Det Ch Insp Nigel Penney said Ms Davies' family were "living through a nightmare and are desperate for news", emphasising that the case remained a missing person investigation.
He added: "We are working hard to find Owami but we really do need the public's help. Owami is very vulnerable and the longer she is missing, the more we worry that she has come to harm.
"As a result of extensive CCTV inquiries, we have a clearer idea of Owami's movements but we still need the public to contact us and tell us what they know."
Correction on 3 August 2022: The Metropolitan Police initially issued incorrect images of the CCTV footage, which the BBC published and later replaced with the correct images.
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