I can see a number of newspaper articles that reference Allen Square, East Street, Bedminster.
There is an archeological report about the former Baptist Church at 177 East St, which includes:
"The records that are closest to the Study Area relate to No. 145 East Street, and an unnumbered property
off Norfolk Place.
The records for No. 145 East Street are for a c. 1870 photographic record of three
buildings in the location of Nos. 143-147 East Street (BSMR 21187), and an observation
of No. 145 undertaken in 2003 (BSMR 21681).
The unnumbered property off Norfolk Place is referred to in the Bristol Sites and
Monuments Record as ‘building on the East side of Allen Square’ (BSMR 21190-21191).
The name ‘Allen Square’ is not recorded on the current OS Map (see Figure 3), it was not
recorded on any of the historical maps consulted during this survey, neither does it appear
as a modern postal address (Royal Mail Postal Address Book, South West Edition 1997).
The building implied appears to be the limestone built house described above, believed to
have been the former location of a clay tobacco pipe manufacturer (Bob Jones, City
Archaeologist, Bristol City Council, personal communication). "
Etheridge, D.J. & Payne, R. (2009) "The Former Baptist Church, No. 177 East Street, Bedminster, Bristol. Archaeological Recording and Monitoring (Standing Building Recording and Watching Brief)."
So Allen Square was presumably on the west side of Norfolk Place. (shown on the map in previous reply).