As far as I can see Eltham has never been a borough in its own right.
Eltham was a civil parish of Kent until 1889 when it became part of the County of London and from 1900 formed part of the Metropolitan Borough of Woolwich. The metropolitan borough was abolished in 1965 and Eltham then became part of the present-day London Borough of Greenwich.
I have a completed grid with the aid of the unchecked letters, but cannot completely crack the theme. I have probably gone horribly wrong since 14D appears as gibbersish in my grid.