You can start work immediately, the nature of the EEA Family permit is that it is valid as a work permit also.
Your employer will apply on your bahalf for a NI number.
You can apply immediately for a residence card, you don have to wait until the end of your permit to do so.
You will receive a letter from Croydon stating your right to immediate employment.
My wife Jet started work a few months ago, and her employer has applied for the NI number for her.
No need to waste time in waiting.
Good luck in your job search...
http://www.bia.homeoffice.gov.uk/sit...s/eea/eea2.pdf