Peter (Timber),
I can't give you a definitive answer on the passport issue.
Normally, just a certified copy would be enough.
Given the wording in the UKBA webpage, I'd be inclined to seek clarification from the British Embassy in Manila. After all, they will be responsible for issuing the FP

I really wouldn't get overly stressed about it. You are legally exercising treaty rights here in UK and by EU law and directives are entitled to have your wife join you. I feel that the British Embassy should advise you given the complications you outlined.
I think requesting certified copies from the Hungarian Embassy here in UK would be perfectly in order.
Whenever you request information please do request urgent priority.

I am not an immigration advisor but I doubt that UKBA can refuse FP for that issue. It's just I wouldn't want to give you anything less than 100% correct info, so do secure info from Embassy.