Upvote:1
It depends. Your place of birth is recorded on your passport. If you were born in UK (or Gibraltar, or the Falklands...), then I believe you could not possibly be a British citizen by descent. However there are some British citizens by birth who this doesn't apply to (for example, the foreign born children of British officials). They would need some further evidence. Therefore, the place of birth field may be sufficient (but is not necessary) to prove British citizenship by birth.
Upvote:2
I assume you are attempting to determine if you can take your infant daughter abroad without her needing her own passport, and relying on her birth certificate/identify card along with your passport to prove that she is a British citizen. I believe you are on tricky ground here. Even if it were technically true that you could determine such a thing, you cannot rely on any immigration agreeing with your determination.
It would be much more sensible to register her as a British citizen, and to get her own passport. This will remove any doubt and enable her to enjoy the full privileges of travel.