Libby, 21, was last seen in the early hours of February 1 after coming home from a night out at the popular Welly Club in Hull.
She was put into a cab by friends, but never made it inside her student digs just two miles away after she was dropped-off around 11.40pm.
Police have said the last confirmed sighting was on Friday, 1 February, at 12.05am on Beverley Road at the junction with Haworth Street.
Her family have also released a new video of Libby having fun and smiling and laughing with her friends at Hull University.
The missing girl is 5ft 7in tall with shoulder length brown hair and can be seen wearing a black long sleeved top, leather jacket and black denim skirt.
Humberside Police have admitted however it is becoming likely that she has come to “harm” and said they have followed up “hundreds of leads”.
“Libby’s disappearance remains unexplained and we must increasingly consider she has come to harm”
Detective Superintendent Martin Smalley, who is leading the probe, said: “Libby’s disappearance remains unexplained and we must increasingly consider she has come to harm.”
He added: “Have always kept an open mind as to Libby’s disappearance, hopeful we would find her and be able to return her home safely to her devoted and loving family.
“Throughout the entire investigation we have consulted with national experts from other forces and agencies as well as river and water specialists and search professionals, to ascertain where Libby may be and understand exactly what happened that night.
“Although we have followed up hundreds of leads and lines of enquiry and carried out intensive searches as part of the investigation over the last four weeks, as time passes by with no positive indication as to where Libby is or what has happened to her.”
DS Smalley added CCTV released last week of four potential witnesses that may help the hunt for Libby.
He said: “It prompted a number of people to call in with information which I am very grateful for. Unfortunately it did not produce any results in identifying the individuals.”
Libby is said to have been turned away from the student nightclub by doormen for being “too drunk”.
She was then put into a taxi to take her home, when she is then believed to have sat on a bench nearby close to the junction with Haworth Street.
It is believed a motorist then stopped to offer help – with detectives saying she was in the area until around 12.09am.
DS Smalley said searches are being focused around the Oak Road playing fields and the River Hull.
And he stressed despite the growing fears for Libby’s wellbeing, the investigation remains “very much active”.
He added: “Oak Road and the playing fields have been an area of interest throughout the investigation with resources deployed and extensive searches conducted. Our searches are continuing, with further searches in and around the River Hull.
“I am aware of speculation and theories as to what may have happened to Libby. These will be considered and explored as part of the investigation.
“CCTV footage has formed a crucial part of the investigation so far, with detectives working non-stop and viewing hours of film to piece together Libby’s movements and thereafter the last sighting. We haven’t released the majority of this footage for operational reasons and to protect the integrity of the investigation.
“Where we are able to, we will share updates as to the progress of the investigation as I understand everyone wants to know where Libby is. “
Libby’s mum Lisa Squire said today: ”It’s now been four weeks without our beautiful Libby. A month of utter heartbreak and despair.
“As a family we are incomplete. We miss her more than we could ever say. We just want her back with us.
“Please if anyone has any information no matter how insignificant it may seem, contact the police.”
Police have been examining CCTV footage taken of a man sitting by his car before appearing to load “someone or something” inside close to the last sighting of Libby.
More than 20 screens in the city centre are showing pictures of Libby.
And police have sent out thousands of leaflets distributed in five languages.