Sarah Everard's family have paid tribute to her, saying she "brought so much joy to our lives".
Human remains were found in woodland in Kent on Wednesday in the search for the 33-year-old, who was last seen in south London over a week ago.
A serving Met Police officer in his 40s who was arrested on suspicion of Ms Everard's murder remains in custody.
The Met has referred itself to the police watchdog over allegations the officer indecently exposed himself.
He is also being questioned over the separate indecent exposure allegation, which the Independent Office for Police Conduct (IOPC) said happened at a fast-food restaurant in south London on 28 February.
Ms Everard was last seen on 3 March walking alone down a main road in Clapham at 21:30 GMT, with police saying it was unclear if she reached her home in Brixton.
After extensive searches, Met Police Commissioner Cressida Dick confirmed "human remains" were found in woodland near Ashford on Wednesday.
A woman in her 30s, who was arrested in Kent on suspicion of assisting an offender, has been released on bail until mid-April.
The arrested man, who works with the Met's Parliamentary and Diplomatic Protection Command, was earlier taken to hospital suffering from head injuries.
He was being monitored in a custody cell by CCTV and received immediate first aid, the Met said.
After going to hospital the officer was treated, discharged and returned to the police station where he is being held after an application to extend his detention was granted at Wimbledon Magistrates' Court.
The IOPC said it was investigating whether Met officers responded appropriately to the report of indecent exposure.
It is one of five investigations being carried out by the watchdog in relation to the disappearance of Ms Everard.
The others include the serving officer being arrested, injured in custody and the Met's actions responding to the initial report of Ms Everard going missing.
Former Durham University student Ms Everard, who is originally from York, was wearing a green rain jacket, navy blue trousers with a white diamond pattern, and turquoise and orange trainers when she went missing.
In a statement, her family appealed for more information to "help solve this terrible crime".
"Sarah was bright and beautiful - a wonderful daughter and sister. She was kind and thoughtful, caring and dependable. She always put others first and had the most amazing sense of humour," they said.
"She was strong and principled and a shining example to us all. We are very proud of her and she brought so much joy to our lives."
The marketing executive's family also thanked friends and the public for supporting them.
"We are so grateful to the police and would like to thank them for all they are doing," they added.
"We are now pleading for additional help from the public."
The case has prompted an outpouring of shock and anger as women across the country share their own experiences of feeling unsafe.
Earlier, Labour MP Jess Phillips read out the names of almost 120 women killed in the UK where a man has been convicted or charged as the primary perpetrator.
Prime Minister Boris Johnson said he was "shocked and deeply saddened", adding: "We must work fast to find all the answers to this horrifying crime."
Since last year on this day, these are the women killed in the UK where a man has been convicted or charged as the primary perpetrator in the case. pic.twitter.com/CTaLOc0F5v— Jess Phillips MP (@jessphillips) March 11, 2021
- 3 March: Sarah Everard vanishes after leaving a friend's house on Leathwaite Road, Battersea, about 21:00 GMT
- 5 March: Met Police are "increasingly concerned" for Ms Everard and make an appeal on Twitter
- 6 March: Ms Everard's family say her disappearance is "totally out of character" as officers search Clapham Common's ponds
- 7 March: Footage taken from a doorbell camera shows Ms Everard walking alone along the A205 Poynder Road towards Tulse Hill at 21:30. Police say it is unclear whether or not she reached her house in Brixton
- 8 March: More than 120 calls are made from the public on the case and more than 750 homes are visited as part of the investigation
- 9 March: A serving officer is arrested in Kent along with a woman who is held on suspicion of assisting an offender
- 10 March: Met Police Assistant Commissioner Nick Ephgrave describes the arrest as "shocking and deeply disturbing". Extensive searches are carried out in parts of Kent. Later in the evening Commissioner Dame Cressida Dick said human remains have been found in a woodland in Kent
- 11 March: Suspect taken to hospital after suffering head injuries while in custody. The woman arrested on suspicion of assisting an offender is released on bail