Hello Brian,
Back in the 1990's I worked with a David Hammill and as rosie99 said it is not a very common name.
The David I worked with died suddenly in 1996 (Reg. Leeds M7c 0921M) he was 46 years old. As far as I can remember he was single and lived with his brother who's name I don't know.
Myself and other colleagues attended his funeral which was held at St Mary's, Woodkirk. We were told the arrangements had been made by his brother and there would be no hymns, music of any kind or comments, just a committal service. Even the Vicar found that strange.
After the Service the burial was at New Wortley Cemetery, Leeds which we went to.
Having been to New Wortley searching out graves for people I know the Cemetery fairly well and remembered roughly the location of David's grave. When your post came up I checked records for Hammill's buried there. There is a Hammill grave in the area I was thinking of but as the records I have do not go as far as 1996 David is not mentioned as being in that grave.
If it will help you in your search those in Consecrated grave 8622 are as follows.
Sarah Jane Kane (71) buried 12/5/1947, widow of 1 Eleanor Street.
Linda Hammill (3 weeks) buried 5/2/1951, daughter of Henry 1 Eleanor Street.
Harry Hammill (59) buried 20/12/1971, Post Office worker of 51 Fairfield Street.
Glady's May Hammill (65) buried 20/5/1987 of 3 Holly Court, West Ardsley.
Leeds Bereavement Services would be able to check if any others are in that grave or tell you which grave David is buried in. Tel. 0113 3788196
Hope this is of interest for you,
Ian