Thanks everybody. I'm trying to map my family as they moved around Birkenhead. I've found an old post from Diggingdeeper in 2009 that shows Seabank Cottages behind the buildings on Seabank Road on the Tannery side. Apparently where Ark Royal Way is now.
I remember that post, but not looked for it as the buildings have changed a bit in the past few years.
What remains of Seabank Road seems to be the passage behind the Halfords Auto-Centre and the building to the south of it. The wall at that point is formed from two shades of light grey brick and is quite distinctive, and it is adjacent to the start of the bus stop pull-in.
Therefore, as you thought, Seabank Cottages would have been between Ark Royal Way and the front of Halfords. A section of the 1876 OS map is attached. Bridge St is now Chamberlain St.
Despite its pleasant sounding name and proximity to the river (the wall would have been where Cambletown Road lies) contemporary reports of the time describe the stench from the mud flats in Tranmere Pool, if I remember correctly.