We used to go there after London matches back in the late 1960s. It was a bit wild. There was a resident band who played the tunes to bawdy rugby songs leaving the clientele to sing along.
It was always mentally full on a Saturday night and a nightmare to get served, so it was wise to get two rounds at a time. Those on the terrace overlooking the Thames would often throw empties into the river. The staff would collect them in a low tide. Those inside would often drop empties on the the ground to smash them.
It was quite scary to get there. It was in the old East London tube line through Shadwell. There were no escalators and it was very deep underground so you had to travel in an antiquated lift up to the surface.
Then you needed to walk along Wapping High Street which was all high warehouses looking like something from a Sherlock Holmes story. I suspect that it will all have been redeveloped now and the ancient tube line modernised.
I did go back a few years later to the Prospect and found it changed beyond recognition. There were security guards around and notices uo about the ban on bawdy songs. The place seemed to be filled with German tourists.