Cos-ham, or Cosh-am? I thought it was the former. How about Bosham, just along the road to Chichester?
Yes, always, always (even the train announcement gets it right).
In Cosham it's a very localised, even within the city, pronunciation of Cozzam mainly on the mainland and among the over 50s. My mother-in-law, Paulsgrove girl, used to say it that way when she was younger but she's lived in Fareham for 40 odd years where no-one says it that way.