General Gordon's family and convalescent home?

I wonder if any of your members can help me with information related to my family history research. It relates to Woolwich rather than Greenwich but I hope this is not too much of an obstacle.

What I am looking for is this:

Does anyone know if a member of General Gordon (of Khartoum)'s family was running a convalescent home for military patients in Woolwich around 1879?

I believe that Mrs Hawthorn, nee Dow, a member of the Enderby family, was campaigning against the neglect and ill-treatment of patients in military hospitals around that time, and I wondered if it might be her.

Any help would be very much appreciated.

Yours sincerely

Dugald Macleod