Detectives are asking anyone who recognises a woman shown on hospital CCTV footage to call Surrey Police on 101, quoting the reference RM/13/4481 or call Crimestoppers anonymously on 0800 555 111.
Police want to speak to her in connection with a number of thefts from elderly and vulnerable patients.
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A woman died as she crossed the road when she was struck by four separate motorists who police believe did not stop.
Patrols including local volunteers have been set up after the grisly finds in Thamesmead in the last month.
Thieves targeted a property in Richmond on Monday afternoon.