Between about 10.40am and 11am on Saturday, May 28, the victim was walking along High Street towards Castle Quay.
The victim then realised her purse containing her debit card, store cards and a quantity of cash had been stolen from her handbag as she walked from McColls to the shopping centre.
The victim’s bank cards were then later used at 11.06am and 11.14am in an attempt to withdraw money from an ATM at Barclays Bank, in the High Street.
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PC Robert Kelly, from the Patrol team based at Banbury police station, said: “We are keen to speak to the man in the CCTV image, as he may have information which could help with our investigation.
The victim has been left feeling very shaken and vulnerable since the incident so it is vital we are able to get some answers.”
He added: “We are appealing to anyone who can help with our enquiries, if you have any information regarding the incident or saw anything suspicious in Banbury High Street on Saturday morning please contact me through the non emergency number 101.”
If you don’t want to speak directly to police you can contact the independent charity Crime Stoppers anonymously on 0800 555 111.