1) If child's parent (one or both) is British, then the child will be a British citizen too.
2) If child's parent (one or both) is not British but has permanent residency in the UK, ie holds Indefinite Leave to Remain or Permanent Residency under European law, then the child will be British also (even if both parents aren't British).
In case of European citizen parents, it doesn’t need to be a formal PR document on the child’s birth date, it is sufficient to have qualified for it and apply later.
3) If the child's parents are both not permanent residents and hold visas, such as Tier 1, Tier 2 etc, then the child will NOT be British, even though it was born in the UK. In such a case a child can be given a dependent visa on his/her parents’. This can be done as a separate application, though it's not compulsory and can be done instead at the time of parents' next application, such as at the time of Tier 1 extension.
3.1) Once child's parent (one or both) secured ILR, the child can be registered as British straight away, even before parent(s) qualify for Citizenship themselves.
3.2) Does the child need to be included in the ILR application? Costing another expensive government fee? The answer is No. Once at least one parent has ILR, the child can be registered as British.
4) What is the difference between 'will be British' and 'not British but can be registered as British'?
In points 1) and 2) the child 'will be British' from birth meaning parents can just apply for his/her UK passport, ie for a passport book: https://www.gov.uk/get-a-child-passport
In point 3) the child will need to be registered as British first meaning submitting a Registration application to the authorities, to a visa application process, paying a fee, waiting for a decision. Once decision has been made - and decision is positive - parents can apply for the actual passport.
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