Thanks Gortonboy and Cati for your swift replies.
I am not sure if this fits because the base of the badge on grandfather's photo is a different shape to the base of the West Kents cap badge.
I have seen on the websites that there is a pre 1919 cap badge for the Herts & Beds regiment but I cannot find a picture of it.
The medical record for Edwin Lee of the West Kents lists him as a Private but on his photo he has a lance corporal stripe as well as overseas service stripes. So would he still be classed as a Private??
Maurella