Hi Bob, I ought to know better than to challenge your statement. However I have copies of 1960's Chesterton's Coastal Ships and I cannot find reference to Rea tugs. However, British Tugs / H M Le Fleming 3/60 does list ports in order + the tugs serving each location, even to 60 tonne Testgarth at Southampton. Also later edition Ian Allan 5/66 "British Tugs" was by Ridley Chesterton.
Not sure if there were later British Tugs editions ... I had to grow up and go out to work!
The 1966 edition mentions tug fleets at Southampton (1 tug) and Avonmouth, Cardiff, Barry, Milford Haven and the 1960 edition has Liverpool included with 1913 Cairngarth still working alongside 1915 Graysgarth.
Hope this might fill a few gaps.