Would a 'technically' British child be stateless if...

[Kelko]

their birth couldn't be registered in the country they were born?

Weird question (and doesn't apply to me or my children), but I found out that in Lebanon only a Lebanese father would give the baby entitlement for its birth to be registered. Therefore, what would happen in the case of a British woman, who isn't married to a Lebanese man, giving birth over there?

To register the birth over here, you'd have to provide a Lebanese birth certificate. If this cannot be done, it seems the baby can't be registered over here either. If the baby isn't registered, how can she/he get a passport or have any rights as a British citizen?

I've had a poke around online and I can't find any legal coverage for children being born in the situation. Would they be stateless or is there another term for them?