The ridiculously named Propaganda Music Canteen in Andover is thankfully renamed the Plush Lounge Bar. Only opens Thursday to Saturday evenings and only one step above a club, as they don't charge admission.
I have submitted a listing for music venue the Rockhouse, even though it does sometimes charge admission when live music is on, as it is open every evening and all day Sundays as a bar.
Meanwhile, the Star and Garter probably needs marking as closed. The whole of the impressive Georgian main building is now a pizza restaurant. There are still some rooms available round the back, and the reception desk for these has a fridge behind it where you can buy a bottle of beer and sit in the courtyard. So technically you can buy and consume a drink, but I don't think it really warrants inclusion as any sort of pub. not least as there is no indoors room. I have placed an explanatory review in case it needs keeping for completeness.
The Railway Club has been posted as closed - it is emptied and for sale, somewhat optimistically still as a social club.