Sabina Nessa, 28, was attacked as she walked through a park in Kidbrooke, south-east London, on her way to meet a friend on September 17.
Her body was found nearly 24 hours later covered with leaves near a community centre in the park.
It is claimed her attacker used a 2ft long weapon to strike her repeatedly before carrying her away unconscious.
Both the MET and Kent Police are searching wooded area along Dundale Road, which is near to Lamberhurst. Both forces have been approached for comment.
A spokesperson for the Met Police said: “Officers are searching an area of woodland near to Tunbridge Wells in Kent as part of the ongoing investigation into the murder of Sabina Nessa in Kidbrooke.”
The news comes as Eastbourne garage worker Koci Selamaj, 36, appeared in court on Thursday [September 30] accused of the ‘premeditated and predatory’ murder of the primary school teacher.
A post-mortem examination has yet to confirm the exact cause of her death but the attack was said to have involved “extreme violence”.
Selamaj was arrested in the seaside town in the early hours of Sunday and charged with her murder on Monday.
A light-coloured Nissan Micra was seized in a leafy residential street about half-a-mile away.
Selamaj, who is originally from Albania, appeared at the Old Bailey before the Recorder of London, Judge Mark Lucraft QC.
Prosecutor Alison Morgan QC told the court it was a ‘premeditated and predatory’ stranger attack and there was no suggestion the defendant knew Ms Nessa.
During the hearing, the defendant, who has already indicated he will deny murder, spoke to confirm his name and date of birth before a timetable for the case was set.
Dressed in a prison-issue green and yellow top, he appeared in court by video link from Wormwood Scrubs assisted by an Albanian interpreter in court.
Judge Lucraft set a plea hearing for December 16 and remanded the defendant into custody.