It's a shame he just missed having his birth registered, you could check for christening records for him in the local area, if there was a father he'd be mentioned there.
My grandfather was an illegitimate child, there's no father on the birth or first marriage certificate but he made one up (poor guy) on his second marriage certificate. I never knew him as he died when my father was a baby.
Don't give up, if there was a father there's a chance you'll find him, just need to rethink your route.