But You have to consider that afaik Hungarian licences are only good for a certain number of years - and that number gets smaller when you're older!

I still remember my neighbour's frustration when he forgot the date and about a week after the licence became invalid he was checked and had to pay a fine - and he was a retired policeman even!

I have just exchanged my licence.
It takes time, but other than that simple.
I did mine at the local council office, the young lady who deals with licences is a relative and speaks English so much easier but doesn't change the process.
I gave her my UK licence, passport and address/residency cards, 5 minutes of key clicking and she gave then all back with instructions to return in 2 weeks. 2 weeks became 10 but in fairness it is possible DVLC in Swansea are receiving a larger than normal number of applications.
I was told I needed a medical certificate which was a simple exam by my doctor, the eye test is a numerical one as opposed to the alphabetical ones in the UK, I read them aloud in English which the doctor doesn't speak but he was happy and signed the paper, (No fee).
Took the medical certificate to the council office, they take the photo there, and even asked if I was happy with it before printing it onto the licence, then it was just a matter of payment, 1500 fts for my old person status. Which is much simpler if you pay by card as it's then and there, cash needs a trip to the Post Office with a yellow check.
10 minute wait and hand over my UK licence and I am now an Hungarian driver. (apparently they retain my UK licence and I may re-exchange the two simply by returning my Hungarian one, if this works in practice I have no way of knowing).

My UK licence was due to expire next year anyway, my new licence gives me 2 year before a medical and renewal.

Thanks, duztee!
I wasn't sure but you confirm it:
For us older people the licence is valid only 2 years, then a new medical exam - even if it is just perfunctory ...
Rather OT:
My German driver's licence I got in 1961 is still valid - just the paper one has been exchanged for a plastic card, no medical, no exam necessary - unless you are taken to court ...

Duztee, that's terrible!

Now we know who that character is who always does 80 in the 50 zone.

Let's hope he knows what "tilos" means!