The incident occurred on Thursday, June 26, between 7am and 7.30am on Houndwell Place on the same side of the road as the old Debenhams store.
A 31-year-old woman was approached by a man who demanded her purse.
When she refused, he punched her in the face causing her to fall and kicked her while she was on the ground.
She then handed over her yellow purse, about 15cm long, which contained £100 in £20 notes, several bank and store cards, before fleeing along Queensway.
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The victim sustained facial bruising and experienced hip and abdominal pain.
The man police are seeking information on is described as black, in his 20s, quite skinny but muscular, with a short beard.
He was wearing a black top, black shoes, and a black hat.
A spokesperson for Hampshire Constabulary said: “Anyone with information is urged to contact the police online or on 101, quoting reference 44250281600.”