I can't find any evidence that HMS Gambia left Wareham Creek for any reason apart from being towed out for scrapping in 1969.
During WWII, many towns adopted a ship and Huddersfield adopted HMS Gambia. These towns raised funds for the adopted ships, sent the crew small gifts and generally supported the ship. These relationships sometimes lasted until the end of the ship’s life. Huddersfield even remembered the ship 50 years after it had been taken out of service - https://www.examinerlive.co.uk/news/...artime-4985877
At the end of her 1958/60 commission, Gambia was sent to Liverpool and one of her last duties was an open day for the people of Liverpool and Huddersfield, about 60 miles away. There are civilians on the ship in the photo, and that was a relatively rare event.
HMS Gambia was in Liverpool from November 29 until December 6, 1960.
After a bit of detective work, a few emails, and knowing things like when Gambia was in Liverpool, the fact there are civilians on the ship, where the shadows are on the foreground bollards, under the turrets and lifeboats, and a few other things, here's what I've got.
So, as far as I can ascertain, the photo is of HMS Gambia at Canada Branch Dock 2, Liverpool. It was taken near midday on Sunday, December 4, 1960.