Detectives from the Metropolitan Police’s specialist crime unit continue their extensive enquiries to find missing student nurse Owami Davies.
Officers have searched houses and parks, viewed hundreds of hours of CCTV and conducted extensive door-to-door enquires, but still Owami, from Grays, remains missing.
Five people have been arrested in the course of the inquiry – two on suspicion of murder and three on suspicion of kidnap.
Detective Chief Inspector Nigel Penney, who is leading the investigation, said: "The sheer scale of this inquiry shows how concerned we are for the safety of Owami.
"With every day that passes that concern only grows and our fear increases that she has come to harm.
"Although this is a missing person enquiry, this is one of the biggest investigations I have ever experienced and that reflects our determination to find Owami for her family.
"Owami has now been missing for over a month and her family are desperate for news.
"We are keeping them fully informed, but finding Owami is the only thing that will bring them any peace and for that we need the public’s help.
"I want to thank the public for all the support we have already received, but I continue to appeal for anything that could assist our inquiry.
"Please call if you have any information - do not talk yourself out of telling us what you know. If you think you may have information about Owami, trust your instincts and call."
Owami, 24, was seen in the early hours of Thursday, 7 July as she walked along Derby Road, West Croydon.
A second unconfirmed sighting has also been reported on the same day, at around 7am, in nearby Clarendon Road.
She had left her family home in Grays three days earlier on Monday, 4 July.
The Met’s Specialist Crime Command is leading the investigation to establish what has happened to Owami.
South Area Commander Chief Superintendent Dave Stringer, said: "I can assure our community that all we can do to find Owami is being done.
"We are working closely with our colleagues in Specialist Crime, who are used to dealing with large, complex investigations and we are providing them all the assistance we can in this extensive inquiry.
"Everyone, I am sure, is hoping that Owami is safe and well and this nightmare for her friends and family will finally end.
"We understand the real anxiety that is currently felt in our community and we have additional officers patrolling to reassure you.
"Please do take the opportunity speak to these officers about your concerns, they are there to help you and answer any questions you may have.
"Lastly, I would like to express my thanks to everyone who has helped us, and is helping us, to find Owami. We truly appreciate the outstanding support we have received from both our community and our partners."
All five of those arrested during the course of the investigation have since been released on bail, whilst the investigation team follow up on further enquiries.
Anyone with information should call the incident room on 020 8721 4622.
Information provided will be handled sensitively and anyone who comes forward to assist officers will be given every support.
Alternatively, information can be provided anonymously to the independent charity Crimestoppers.
They are separate from the police, they do not trace calls or monitor IP addresses. To contact them, either call 0800 555 111 or visit www.crimestoppers-uk.org