@HirplesWithHaggis
Thank you, food for thought. I am aware that DC raised bilingual from birth have advantages later learning more languages, does this not include BSL? I wonder if there's any research.
(But must pop off to make food.)
So, baby signing, and BSL are not the same thing. Baby signing is based on Makaton, or in some areas SignAlong (both are similar and Makaton is the more common one). These are NOT the same as BSL. British Sign Language, as you say is something you could be "bilingual" in. It totally replaces spoken language so it's the full English language in signs.
Makaton, which is what is used for baby signing, is part of what is known as a Total Communication approach. It is used by hearing children, not deaf children (they would use BSL), and it is used to augment their understanding of what is being said to them. You only sign key words in a sentence that you really want to get the meaning of across, and you sign it as you say it. It does not at any point replace language and is only ever used with the spoken word.
This is why, for a neurotypical child, there is no reason to need to sign, nor would it give them any advantage or a second language, because they would actually just be understanding your spoken word anyway.
If you wanted your child to be "bi lingual" in signing you would have to learn and teach them full British Sign Language, which as I've explained is totally different both in how it looks and how it's used, to baby signing / Makaton.
Hope that helps!