Either your date is slightly off, or the registration authorities made an error, or were very slow in registering the birth, but it wouldn't have mattered much in this case, because there's only one birth that it could be, and if you had applied to the UK General Register Office ( GRO ) with the information that you had, they could have easily found the correct birth registration.
http://www.gro.gov.uk/gro/content/UK GRO Army Birth returns 1916-1920
Sydney H.N. Roberts...Station Gibraltar...Year 1916...page 18