Eltham and Woolwich would both now come under the London Borough of Greenwich, although at those times they would have come under LB of Woolwich (which no longer exists). You also have the problem of different constituencies. I think at that time Eltham was covered by Woolwich West (it certainly was in the 70's) and Woolwich would have come under Woolwich West or East, according to where you are after. Try writing to the Town Clerks Dept, Woolwich Town Hall (This is not a misprint!), Powis Street, Woolwich SE18.
PS I lived in Eltham from '59 - '83 if thats any help.