A 36-year-old man will appear in court later charged with the murder of primary school teacher Sabina Nessa.
Koci Selamaj, from Eastbourne, East Sussex, was arrested in the seaside town in the early hours of Sunday, and a light-coloured Nissan Micra was seized in a residential street around half a mile away.
He will appear before Willesden Magistrates' Court on Tuesday.
Ms Nessa was killed as she walked through Cator Park in Kidbrooke, southeast London, on her way to meet a friend on 17 September.
Her body was found nearly 24 hours later covered with leaves near a community centre in the park.
The suspect is understood to have been working as a food delivery driver in Eastbourne and is thought to be originally from eastern Europe.
On Friday, hundreds of people - including her sister - gathered for a candlelit vigil organised in Pegler Square, Kidbrooke, in her memory.
Jebina Yasmin Islam, Ms Nessa's sister, broke down as she addressed crowds.
She said: "Words cannot describe how we are feeling, this feels like we are stuck in a bad dream and can't get out of it - our world is shattered, we are simply lost for words.
"No family should go through what we are going through."