I looked on Google Maps while in Barcelona, and it showed that the History of Barcelona Museum was down or near Via Laietana. So we walked down the road (which we had earlier been on).
But we ended up walking as far as Port Vell first (which is beyond the Correus i Telègrafs / Central Post Office of Barcelona building.
So after we were finished looking around the harbour, walked up a side road that took us past the palace, and headed up a side road round the back with the museums, and eventually found the museum in the end.
Wedged building at Via Laietana, 39.
Enginyers
At the junction of Carrer del Dr. Joaquim Pou.