Police said she was found dead on East Sussex beach at Bexhill near Galley Hill at 6.20am on September 18.
Her body was identified that morning and her mother was visited and informed by Metropolitan Police officers later the same day.
Police released a statement on Tuesday outlining their investigation after a petition and social media users claimed they were not investigating her death thoroughly because she is black.
Her death has been deemed as “unexplained” by Sussex Police, with a postmortem determining she died by drowning.
Officers searching the area where Ms Olusegun was found located her phone and slippers.
They said they searched her room at her placement and were in the process of a forensic examination of her devices and a detailed review of her phone records.
Police added that CCTV from the local area showed Ms Olusegun walking to the beach at around 1.30am alone with no evidence of others being in the vicinity.
A pathologist found Ms Olusegun had died from drowning with “no evidence of violence or any internal or external injuries”.
Senior Investigating Officer Detective Inspector Pippa Nicklin said: “I have spoken with Blessing’s mother and explained we remain absolutely committed to finding out the facts of what happened to Blessing.
“This is a very distressing time for her and we are keen to do everything we can so that hopefully she may gain some closure over the death of her much-loved daughter.
“Although there continues to be no evidence of a crime we are still carefully and fully examining all the circumstances leading up to Blessing’s death, from her arrival in Bexhill, to her leaving the house where she was working and walking to the beach.
“It has been reported that we have not properly investigated Blessing’s death because of her ethnicity and we strongly refute these claims.”
The force added that all evidence collated will be submitted to the Coroner, who will set a date for an inquest in due course.
“We need justice for Blessing and her family. What actually happened?”
Following recent vigils, a union claimed Ms Olusegun’s death had not had the same response as Sarah Everard’s, citing discrimination towards people of African heritage in public services.
Cheryl McLeod, Lewisham TUC president, said: “We mourn Sarah Everard… However, there is another death within our community, who like Sarah, was a woman who was walking alone.”
Lewisham and Southwark TUC issued a statement which said: “We need justice for Blessing and her family. We need fairness and we need democratic accountability of the police and government.”