Taken some time between 1963 and 1975.
Photo by Martin Hulbert, reproduced with kind permission.
A big thank you to all the Facebook group members who identified the location to be St Pauls Square. And many thanks to Alan Newman for narrowing it down further to be on the corner of King Street and Astley Street off St Pauls Square. I've attached a screenshot from google street view of an old image showing the community centre before it was demolished and rebuilt into a block of flats.