I have been trying to trace my Kilford's for a while now and someone did a 1901 census look-up for me a while ago and found your Kilford's living in the same area as mine, Beckenham, and my Kilford's Selina and Alfred and their children Alice, Ethel and Selina I thought might have a connection to yours like Walter and Alfred were cousins or something, but i haven't been able to figure it out yet, and was trying to trace Walter's ancestors. Have you got any further from Walter's parents?
Here is my tree, just to give you a rough idea of what i am on about and see if you can make a connection:
Robert Kilford, born 1791 in Shrewton. Married to Catherine ? from Maddinton and had:
Elizabeth (Had a daughter called Charlotte) born Maddington 1823.
George (Married to Elizabeth Longin 1856 firstly, and then to Hannah ?) born Maddington 1830.
Joseph (Married Mary Cole 1859) born Maddington 1829.
Joseph and Mary had the following who were all born in Shrewton:
Alfred, born 1863.
Alfred married to Selina Elizabeth Burford (Fron Rochester, kent)and they had:
Ethel Maud was born 1893/1890 in Camberwell, Surrey,
Selina Elizabeth was born 1892 in Camberwell, Surrey,