Ah, sorry, I just realized where my previous post was unclear. I was trying to illustrate how ridiculous the HO's policies are, because the kind or private insurance they claim to need to see doesn't exist in the UK. However, anecdotal evidence from other people applying indicates that a good cover from a UK company will suffice for the HO's purposes, so there's no need to get significantly more expensive "expat" insurance from a foreign country.
Also, I don't know if they're doing this part correctly (as they seem to be deliberately missing the point re: NHS access in general), but it is not YOU that needs the insurance; it's your spouse. [See Immigration Regulations EEA 2006.] If you want to play it safe, you get it for both of you, but it's most important that she has it.
It is also worthwhile to perhaps enlist the Hungary SOLVIT to get clarification on this issue since, by law, your spouse is covered by the NHS, and can prove this through an NHS medical card, and nowhere in the Directive does it actually state that "comprehensive sickness insurance" has to be PRIVATE, and thus cannot be the NHS. [This is an HO invention.] This, however, only if you've got time to spare and aren't planning on leaving the UK soon--the 'quicker' solution is to comply with the HO's unclear demands.