A certidão de nascimento é aceita quando você entra no Reino Unido?

Como GayotFow não é mais capaz de fazê-lo, elevando seu comentário a uma resposta:

With you as the primary, the child has derived rights as a family member which can be established by the birth certificate and expired passport. You may have to wait a while while they study derived rights but I don't see a big problem.

A diretiva do Home Office em Direitos de livre circulação: familiares diretos dos nacionais do Espaço Económico Europeu (EEE) Versão 5.0 na página 6:

Family members who come under regulation 7(1)(a), (b) and (c) of the Immigration (European Economic Area) Regulations 2016 (the 2016 regulations) are often called ‘direct’ family members.

The following can be considered as direct family members:

• spouse or civil partner
• direct descendants of the EEA national or their spouse or civil partner who are:
  → under the age of 21
  → dependants of the EEA national or their spouse or civil partner

Direct family members have an automatic right of residence in the UK for as long as they remain the family member of that EEA national and that person is either:

• entitled to reside in the UK for an initial period of 3 months
• a qualified person
• has a right of permanent residence

Certidão de nascimento pode ser usada para imigração com pais.

Travelling with children

You may be asked at the border to prove the relationship between yourself and any children travelling with you, if you don’t seem to be the parent, eg if you have a different surname.

You can prove this with:

1. a birth or adoption certificate showing your relationship with the child

2. divorce or marriage certificates if you’re the parent but have a different surname from the child

3. a letter from the child’s parent giving permission for the child to travel with you and providing contact details, if you’re not the parent

Extraído de: link