I think your assumptions are correct.
The photographer is looking towards Woodside. The Town Hall clock tower can be seen in the background above the roof of the Bedford lorry.
The traffic lights would appear to be at the junction of Waterloo Place, so the pubs on each corner would be the Shakespear and Prince Alfred. They are described, with photo's, in another thread in the Pubs section.
Cammel Lairds Main Gate is behind the photographer.
The photo was taken before the bridge was widened.
The best way to describe the location of that junction now is that it was where the traffic from the eastbound Borough Rd flyover joins the southbound Chester St traffic.
Attached is a section of the 1964 OS map, before the tunnel approach works, and a photo from 1969, looking south down Chester St showing the roadworks and the rebuilt railway bridge. I think the pubs would have been just over to the right, behing the beer tanker. (I bit ironic, don't you think?). The bus had missed the diversion sign, and was re-joining the traffic by crossing the central reservation.