It was parish church up until the Luftwaffe bombed it in 1940; the remains were demolished in 1956 and after that Christ Church became the Clifton parish church.
Until that point there had been a church on or very near this site since at least 1154, from what I can see on ChurchDB and ChurchCrawler...
Here's a snap of what the last building that stood here used to look like from the Bristol Archives, and here's an earlier one.
GPS Coordinates:
51.45376, -2.61480
Location: Cliftonwood
