Sorry for your loss.
I carried my dad’s ashes last year on a BA flight from Singapore (where he died) to the UK. I had the cremation permit / certificate and death certificate, which weren’t needed in the end. The local funeral director in Singapore gave us a plastic urn which resembled a time capsule to enable easy xraying.
I would absolutely follow whatever requirements are in place in Hungary - I think the British Embassy should be able to advise. The below suggests ‘minimal bureaucracy’.
https://www.gov.uk/government/public...ackinformation