Jordan McSweeney had followed a number of women on the night he attacked the law graduate.
A sexual predator described as a “danger to any woman” has pleaded guilty to the murder of Zara Aleena.
Jordan McSweeney, 29, also admitted sexually assaulting the 35-year-old law graduate as she walked home from a night out in east London last summer.
Ms Aleena died from multiple injuries after she was kicked and stamped on by McSweeney, from Dagenham.
She was discovered by passers-by in Ilford in the early hours of 26 June.
She was partially naked and struggling to breathe, and was taken to hospital where she died later that morning.
Ms Aleena’s family, some of whom were in court, described her as “independent, big-hearted and a joy”.
Her aunt Farah Naz had said her niece had been conscious of the dangers for women after recent high-profile cases, but she had felt safe walking in the community where she was well known.
CCTV footage recovered by police showed McSweeney following a number of women that evening.
At the time of the killing he was on licence, having been released weeks earlier from prison. He had been serving a sentence for criminal damage, racially aggravated harassment and unauthorised possession of a knife in prison.
Prosecution barrister Oliver Glasgow KC described the assault as a “stranger attack on a lone female late at night making her way home”, adding that Ms Aleena “stood no chance of survival”.
The Crown Prosecution Service said McSweeney “was intent that night on finding a woman to attack”.
After the killing, other CCTV captured him returning to his caravan in Dagenham, where police recovered Ms Aleena’s bloodstained clothes.
After his arrest, McSweeney refused to answer questions and told officers he had attention deficit hyperactivity disorder (ADHD).
The Old Bailey was told McSweeney has 28 convictions for 69 separate offences including burglary, theft of a vehicle, criminal damage, assaulting police officers and assaulting members of the public while on bail.
Sentencing will take place at the Old Bailey on 14 December.
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