I'd try outside The Fleece overlooking the river. I think you'd fit in fine. Usually a bunch of people there who join in together and sing and play. The Fleece usually has stuff going on in the front bar (small and busy), main bar and the outside terrace so lots of options.

You might also try starting something off in a less used pub and you might attract people to join. My wife and I had a really enjoyable evening some years back in the back bar of the Golden Lion. There were some members of Jacks Rake (band from Sheffield) who had 'commandeered' the place for the evening to enjoy some tunes together much to the enjoyment of a bunch of listeners but were happy to have other people join in so we did. Great fun. I looked in this year but nothing was going on there. So a 'band' or group of people can work well to set things off.

Station Inn is also welcoming and people join in together. Front bar is pretty small but had a fluid collection of upwards of 10+ musicians but with a basic nucleus of a group of people.

Even the Black Horse could accommodate 4 people easily. It can go through quiet periods and would work with a group of people. I shared a pleasant hour sharing some songs with a duo there this year.

Think you'll find it easy to find plenty of spots to fit in.