These nearest houses were originally called Chapel Row; they're an extension of the western end of Dowry Square, built 1725-1727. Most of the houses in this area were built from the 1720s onwards as the popularity of the Hot Well caused a demand for lodging space closer than College Green, where people generally stayed before.

Number 262 here, the closest, is presumably owned by the same people who own the little plot of ground that's for sale, given that it's basically at the end of their back garden.

It was called Chapel Row because a chapel used to stand in the middle of this terrace, long before Carrick House was built at the far end.

On the ever-helpful Church Crawler you can see some pictures of the original chapel Dowry Chapel, and its successor, St-Andrew-the-Less. St Andrew (-the-Greater) was of course St Andrew's in Clifton Village.

Pevsner apparently said of St-Andrew-the-Less:

is an unforgiveable crime against the architecture of Dowry Square and chapel Row. Of no value either in its own Gothic forms. The spire is particularly nasty.

Personally, I thought it looked rather nice, but I'm used to Bristol's jumbletechture. It definitely lasted until c. 1963 as there's a picture of it around then (in the background of the devastation wrought by the demolition to clear the way for the Cumberland Basin Flyover System) in Hotwells - Spa to Pantomime.