Hi Geoff,
I found this one listed in the 1857 Harper’s Directory. I wasn’t sure where New Street Place was, but it transpires it was what later became Great Western Road running from the Knapp (the triangle in front of the Compasses and the Welsh Harp) up to Alstone Mill (where Waitrose garage car park is now). It isn’t marked on the 1855-7 Old Town Survey map, so I am not sure exactly where it was, but there weren’t many buildings there then (e.g. only one Burton Cottage).
Regards,
Alan Jones