fast fusion thanks for your suggestion, sometimes there are people that are local to these areas and they would have more of an idea than an outsider (me) where a possibly burial place may have been. I know when I have helped others with this sort of question I can offer local knowledge.
Thank you Carol for your 2 links, that was an interesting post with someone else with connections to Fairmile House, also the piece about whether it was in Hampshire or Dorset.
Thank you abelmabel for your suggestion, I think a very important point. This lady lived, as mentioned, Sandbanks Dorset and died at Christchurch, so more possible a burial in her home town to be looked for first I think.
Ewan