The Home Office has confirmed on its website that citizens of EEA countries can travel to the UK using their national identity cards or passports.
Non-EEA family members
If your family member is a non-EEA national and does not have any documentation issued under the Directive certifying that they are your family member, they should apply for an EEA family permit before entering the UK.
Even though the Directive says that getting documentation is not necessary, it is certainly strongly advised for any direct family members who are non-EEA family members. It will definitely be necessary for any extended family members to obtain the EEA permit before arriving in the UK, as the UK government must satisfactorily assess that your family member qualifies to come to the UK under EU law prior.
If your family member is a non-EEA national and has an EEA residence card issued by another EEA country (on the basis that they have spent time with you as your family member in another EU state) they should be allowed to use this card to enter the UK. However, in guidance for employers about avoiding penalties, these cards are not mentioned, so it is advisable, if your family member needs to work, to obtain a residence card once they are in the UK. You will either need to be entering the UK with your family member or you will need to be in the UK already. If your family member(s) are intending to come for more than three months, you may also need to show that you will be exercising a right to reside or, if you are already in the UK or that you are exercising a right to reside.