The death of Saima Ahmed is unexplained after her remains were discovered in January at Gogarburn Golf course on the outskirts of Edinburgh, 400 miles from her London home.
She is believed to have travelled to the city by train on 30 August last year, with unconfirmed sightings in the Portobello area.
But her family still do not know why she would make the journey to Edinburgh, where she had no known links.
A year after her disappearance, Sadat Ahmed, 33, described her behaviour as “out of character” and urged anyone who may have seen her to contact police to help them “fill in the gaps”.
Mr Ahmed, who last spoke to his sister on the morning she went missing, said: “It’s tough being here but you have to do everything you can to provide the answers. It’s been really difficult for everyone. It’s now one year since she went missing and we have no idea what happened and why she travelled here.
“It’s been really difficult for my parents with no answers, and it’s hard to get closure.”
The Independent Police Complaints Commission (IPCC) said two Metropolitan Police officers had been notified they were under investigation for gross misconduct and three officers were served notices for misconduct.
The investigations are in relation to the conduct of the investigation and how information and lines of enquiry were handled. The IPCC stressed the notices did not imply guilt.
Ms Ahmed, a 36-year-old librarian, left her home in Wembley and was thought to be on her way to work but never arrived.
Instead she boarded a train at Wembley Central station and travelled to Edinburgh, via Hemel Hempstead and Birmingham.
Her body was found by a resident living near the golf course nearly five months after she went missing. Her brother, who insisted there was nothing to suggest she was planning a trip, added: “Everything was completely normal.
“There was nothing out of the ordinary and she was meant to be going to work as normal. She had never missed a day of work. It was very strange.
“She never talked about Edinburgh. I think maybe she planned to go – maybe not this far – for a trip to meet someone.”