The three-button cuff flap was very uncommon for British police forces. In Hampshire, however, it was definitely worn by the Southampton Docks Police / Southampton Harbour Board Police
See an 1890 photo at
https://www.btphg.org.uk/?page_id=4109 but note your photo looks like its from the 1870-1880 timeframe, so the details such as cut of the tunic could be slightly different, even if they are from the same force.
Winchester had it's own force during this period - the Winchester City Police. May simply be he's a member of that rather than the county constabulary - can't find any pics of their early uniform unfortunately.
T