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Unless you are a Union citizen or UK national right holder, your children with SA passport wouldn't be eligible. A UK national right holder is a UK citizen exercising treaty rights in the UK.
Being a UK Passport Holder is not the same as being a UK National Right holder
You can be a UK Passport Holder but not a UK National Right holder
You can only be a UK National Right holder if you have for example worked in another EEA country exercising Treaty Rights and then returned to the UK in which case you become a UK National Treaty Right holder
A UK citizen is a Union citizen only when the UK citizen exercises his/her rights in another EEA country
Yes that is correct and if you then decide to return to the UK, the rights exercised in the EU country you settled in can go with you and your kids to the UK. When this happens you would be regarded as a UK national with treaty rights.
Please can you rate? I don't get paid for helping you if you forget to rate
Ok. Look forward to speaking to you.