They have the passport of their birth country (if they have one) because a) when that country became independent their nationality changed and b) they were, at that time, given Indefinite Leave to Remain (ILR) in the UK. They didn't need to change their nationality, they were (and still are) legally entitled to live in the UK.
Of course, some of them might never have had passports... And many might not have been aware of the 2014 change to the legislation...change by Statutory Instrument isn't commonly heavily publicised, You might only become aware of it when it personally affects you. Like when it means you lose your job, can't rent a property or open a bank account.As has been experienced by some of the Windrush Generation.