Friends and relatives have issued urgent appeals on social media to help find the 33-year-old who has not been seen since leaving a friend's house in Clapham, south London, at around 9pm on Wednesday.
A cordon has been put in place on the A205, near the Poynders Court housing complex in the Clapham area, but police would not confirm whether it was related to the search.
On Tuesday two police officers with sniffer dogs were seen searching outside the nearby Oaklands Estate and gardens in surrounding streets.
Other officers were lifting covers and searching drains along the A205.
Ms Everard, who is originally from York and attended Durham University, left her friend's flat in Leathwaite Road in Clapham at around 9pm on to the A205 South Circular. She is thought to have walked through Clapham Common towards her house in Brixton in a journey which should have taken around 50 minutes.
Her family have said it is "totally out of character" for her to disappear like this.
Detective Chief Inspector Katherine Goodwin, who is leading the Metropolitan Police investigation, said there was no information to suggest Ms Everard had "come to any harm".
She said: "We've released two new images of Sarah as we continue to search for her.
"Please take a look at them and consider if you saw her on the night she went missing. I am interested in hearing from people who may have been in the area from 9.30pm onward."
Ms Goodwin added: "I want to remain clear that at this time we have no information to suggest that Sarah has come to any harm and we retain an open mind as to the circumstances.
"We share the wish of her family and friends to have her back safely with her loved ones."
Women living in the area near where she vanished told reporters they had been warned by police to be extra vigilant.
Scotland Yard said no official advice was being given to local residents, but it would remind them of "normal personal safety advice".
Investigators are not currently linking the disappearance to reports of women being followed in surrounding areas.
The Met said it had received more than 120 calls from the public and had visited 750 homes in the area as part of the investigation.
Ms Goodwin said: "We have seized a number of CCTV recordings but we know that there are likely to be many more out there.
"Please, even if you're not sure, check your doorbell or CCTV footage just in case it holds a clue. I'm also asking delivery drivers or anyone with dashcam footage who would have been in the Poynders Road area at approximately 9.30pm on Wednesday to come forward."
The investigation is being treated as a missing person inquiry, but is being led by the Met's Specialist Crime Command due to its "complex nature" and concerns for Ms Everard's welfare, the force said.
She was last seen wearing a green rain jacket, navy blue trousers with a white diamond pattern, and turquoise and orange trainers. She is thought to have been wearing green earphones and a white beanie hat.
In an earlier statement, Ms Everard's family said: "With every day that goes by we are getting more worried about Sarah.
"She is always in regular contact with us and with her friends and it is totally out of character for her to disappear like this. We long to see her and want nothing more than for her to be found safe and well.
"We are so grateful to the police and all our friends for all they are doing.
"We are desperate for news and if anyone knows anything about what has happened to her, we would urge you to please come forward and speak to the police. No piece of information is too insignificant."
Anyone who has seen Sarah or who has information that may assist the investigation should call the Incident Room on 0208 785 8244.