He is entitled to support from SS.
He is entitled to claim UC as a 16 year old.
He is not entitled to force the mother of his underage girlfriend to become his parent, to feed, clothe and house him.
Moreover, council housing is a tricky thing. If he is living there, that lovely new home they've just been offered is no longer suitable for their needs and if the council were to learn of the existence of a male 16 year old 'living' with the family, the offer would be withdrawn because they would not be allowed to make a fifteen year girl share with an 'adult' male, whether a sibling or, as in this case, a random boyfriend. And no, saying he would sleep on the couch would not be sufficient to prevent this insistence upon the offer being withdrawn and being placed back on the list for a property with another bedroom. It's a material fact - one that they would have no choice but to act upon, same way if a child were to leave the home in between offer and start of tenancy, any offer of a larger property would be withdrawn and they would be placed back on the list for a smaller one at any point up to the day of signing the tenancy agreement.
And there's that little thing of teenage hormones. He's her boyfriend. He's going to want to fuck his girlfriend - it's a natural urge. And her hormones are likely telling her the same - have sex. Have them under the same roof and they will find a way - having been a teenager, they'll find a way even if they don't have the ease of access of the house they both share, but it'll be all the quicker with the two of them living in the same place.
Having him removed enables him to get support, means the OP's housing issues are not worsened, keeps that appropriate distance for a bit longer - and reduces the chances of the DD being pregnant before she takes her GCSEs.