Extract from a DHB publication of 1931, the year that the Lady Savile was introduced.
One also notes from this publication that Sir Leopold H. Savile K.C.B. was the Admiralty representative on the Harbour Board at the time and it seems reasonable to suppose that the vessel was named in honour of his lady wife.
This follows the contemporary DHB policy of naming Harbour Board vessels in similar vein e.g. the tugs Lady Brassey and Lady Duncannon.
Interesting to note that eighty years ago the train service was such that it was possible to disembark by tender from an anchored liner and be in London within two and a quarter hours.