For soldiers, if he served after January 1921, his records would be with the Ministry of Defence.
(A later date applies for officers)
If he joined in 1916, it is likely he was born prior to 1901. The Ministry of Defence has issued an aid for all the files they hold with birth dates prior to 1901, which lists names, dates of birth and service number
Details in the FIBIS Fibiwiki page British Army, section Army personnel serving after January 1921
http://wiki.fibis.org/index.php/British ... nuary_1921Cheers
Maureen