Deputy Mayor Stephen Greenhalgh says often people only go to police stations to hand in lost property, so Post Offices could provide a solution in providing police services, while cutting costs.
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George Michael died in December last year at the age of 53.
PC Keith Palmer, 48, stabbed by Khalid Masood while on duty in the grounds of the Palace of Westminster last Wednesday.
Those gathered on the bridge fell silent at 2.40pm - the time the first call was made to police exactly seven days ago.