Can a non EEA family member work right away in UK?

[MHG]

As you are Filipino and only have Czech residency not Czech nationality then I think you will have to apply for the EEA family permit before you will be allowed to work.
Iain

Although I am not British nor living in the UK I know that you have to apply for the family permit since you´re not an EEC citizen !

The EEC right to live and work in other EEC countries is clearly restricted to EEC-citizens. All EEC member countries handle it the same way (wouldn´t make sense if not, eh ? )
Being a citizen of a country outside the EEC excludes you from this right - no matter where you live and whose country´s residence permit you have !!!

I`m German (and live in Germany) and e.g. in Germany there´s no such thing like a "family permit" and we simply have a corresponding residence status indicated on a visa-like sticker in the passport (and the residence status is of course listed in the Alien registration office´s computer)