British nationality law does not prevent a person from holding another nationality in addition to British citizenship, but some other countries are not so relaxed about it. Several EU countries prohibit dual citizenship, such as Austria, Lithuania, Estonia, Netherlands, Slovakia and Norway. This leaves some EU citizens facing a difficult choice between retaining their current citizenship or changing to a new one. Surrendering citizenship is a major step and has serious consequences – for children as well as the person themselves.
British citizens in EU countries face a similar choice. If they wish to acquire permanent status in their country of residence, they may have to obtain a visa or pass new post-Brexit immigration checks imposed by the UK on EU citizens entering the UK. Their children would lose the right to British citizenship by descent.