The family of a British student, who disappeared a day after Christmas, raised concerns about her life after they found a suicide note she left behind before going missing from near her home in Gorleston, Norfolk.

The news comes a day after police scaled back the search for Sophie Smith after exhausting all lines of inquiry. Norfolk Police said the 21-year-old had been suffering severe anxiety and depression and had also received treatment for her mental health.

"We know from speaking to her family that Sophie had previously spoken about her intention to enter the sea to take her own life," Will Drummond of Norfolk police said Wednesday. "Sadly, we can also confirm that Sophie had left a note and messages for loved ones, outlining her intentions."

"We have carried out comprehensive enquiries since her disappearance on Boxing Day. The last and only CCTV image of Sophie was at 3 a.m. on Boxing Day running in the direction of the beach. All other enquiries since this time have proved negative," he added.

Smith was spotted on CCTV heading towards the beach shortly after leaving her home in Avondale Road, but a search of the area did not yield any clues to her whereabouts. The police, coastguard, Norfolk Fire and Rescue Service and Norfolk Lowland Search and Rescue have all assisted in scouring the area.

Smith's mother, Lynn Shaw, said she and her family "fear the worst." 

"In our hearts we hold every hope she will return safe and well. However, as a family, knowing the troubles she was experiencing, we do fear the worst for our little girl," she said.

The mother added: "Sophie had openly discussed how she was struggling and was receiving treatment. I would urge anyone suffering anxiety or depression not to fight that battle alone and seek help. Sophie's step-father Kevin and I would like to thank the public and police for their continued support and dedication in searching for Sophie."

While announcing the scaling back of the search, a spokeswoman for the police said: "We have been in close contact with Sophie's family since her disappearance who have been updated on every stage of the police investigation. In these cases updates are usually provided to a single point of contact who in turn can update the wider family and friends network."

Despite the police scaling back the search, volunteers have come forward to help find Smith. 

"We continue to stay strong and positive. I can not put into words how overwhelmed and grateful the family and I are for the amount of support we have all received from friends, family and strangers, it truly is remarkable," Smith sister Sarah Knowles said.

"I can not thank each and everyone of you for the kind words, shares and sheer determination to get my sister home safely that you have all kindly shown to us. We can only hope and pray that Sophie is found soon."