Read the posts before yours, most of them are making it clear that it would not work anyway as there are serious practical problems with the idea.
It is a pretty natural thing for the first thought of a young lad (or older lad) with a pregnant girlfriend abroad in a third world country, for that thought to be suspicion of the foreign healthcare system.
The baby will be British anyway that is a simple FACT! all they need is to get married or to get a DNA test, the Embassy may insist on a DNA test even if they get married but if it comes back positive the kid is BRITISH doesn't matter what colour the child is.
And just today I've been asked for help in an almost identical case to advise a young 24 year old Scottish lad who is working over there whose partner is pregnant in spite of being on the pill, one of their first concerns was making sure the baby got British Citizenship and they had the same idea, it is a pretty natural reaction if you come from the UK.
Lastly what "colour" would you expect the baby to be in order to be British?
Jim