Yes, a radar tower certainly stood in that position in the 1950's. Also in this picture, to the right of the cables, is the Rhodesia Castle - not a usual visitor to Liverpool, but here in August 1960 for work which included the extension of her funnel.
The tower you can see between the cables was originally a navigation light with a fog signal. Known to the dockers as the Bootle Bull.
The existing radar tower was built in the 1970s and also incorporated the port radio and pilot control centre.
This has now been abandoned and port radio is located further inland on the Seaforth dock.