What to expect when applying for EEA FP on arrival

[johnfm]

(tl;dr) What can I expect when applying for an EEA Family Permit on arrival in the UK?

Full story:
I'm a dual citizen of Australia and the US, and am moving to London after being offered a job there. My husband is a dual citizen of Greece and Australia, and my offer of employment is based on by right to work as the spouse of an EEA national.

Due to some bureaucratic nonsense in Greece (involving his military registration number and exemption from mandatory service) my husband is unlikely to have his Greek passport or national ID card when we arrive in London later this month.The only proof of his citizenship we have is is Greek family record and birth registration, essentially the Greek equivalent of a citizenship certificate. These state unequivocally that he is a Greek citizen.

I applied for an EEA family permit from Australia using these documents, but my application was denied. They said they would accept only a passport or national ID card. I've looked through the Regulations and it's clear that immigration officers *must* consider alternative evidence. We're stopping in Greece to try and resolve this whole situation, but I doubt it will be productive.

We've been advised to try our luck with applying for the EEA family permit on arrival in London. We'll be arriving together, and have all of our paperwork in order, but can't find any information about the process of applying at the airport, particularly without a passport or ID card. Any information or insights into what I can expect would be appreciated!