In the documents you must provide page, the only requirements are:
You must show that your EEA family member has a permanent right of residence or is one of the following if they’ve been in the UK for more than 3 months:
- working, for example an employment contract, wage slips or a letter from an employer
- self-employed (for example contracts, invoices or audited accounts with bank statements) and paying tax and National Insurance
- studying, for example a letter from the school, college or university
- financially independent, for example bank statements
Your family member must have full health insurance (comprehensive sickness insurance) if they’re studying or financially independent.
The guide to supporting documents has more examples of documents you can show.
The registration certificate is not listed, so it is not necessary, although it might help. The guide to supporting documents (PDF) also does not list the registration certificate.
However, your question implies that you are already in the UK. If that is true, you only need an EEA family permit if you want to leave the UK and re-enter. To remain in the UK, you should apply directly for a residence card.