As my partner and I are unmarried he is considered to be an extended family member. According to the Home Office guidance for EEA extended family members do not have an automatic right of entry or residence.
"Rights of an extended family member
Extended family members do not have automatic rights to enter and reside in the UK. Under regulation 7(3) of the regulations, an extended family member has the same rights as a direct family member, providing they continue to satisfy the conditions of regulation 8 and they have been issued with:
an EEA family permit
a registration certificate, or
a residence card.
The above documents must remain valid and not have been revoked.
The conditions the person must meet to be considered a family member are set out in regulation 8."
Therefore, I believe that any period I remain in the looking for work UK after the date my family permit expires would be unlawful.
I also wonder what date they consider to be the date we first started looking for work, as we applied for the initial visa on the basis that we intended to look for work in December last year, however, we have only just arrived back to look for work now.