good dilemma!
Imperial is rather selective, you got in! congrats!, (how about this as a third option?) why not try engineering for a whole year, work at it. (in parallel, if you have the energy, do a UCAT/BMAT or whatever it is this week) so that you could transfer to a UK Med school, Dundee, Kircaldy?
the path to be a doctor is rather long, can be windy (as in, it doesn't need to be straight, not 'breezy') having a year of engineering would just make you a better doctor, more able to specialise in whatever eventually takes your fancy.
Overseas med schools, I have friends who did a year in Warsaw, then took a year off, now re-starting there. I'd be cautious about some med schools whch are outside the EU, they might work - but that's where your question of reciprocal registration with UK GMC is very relevant. Apart from being in the soon-to-be-frenemy EU, with future worries about recognition of qualifications!? need some better qualified people to comment on your dilemma/trilemma
HU as a country for study seems reasonable. Isn't it a bit locked-down at present?
My HU friend said this when I asked : Borders are closed starting 1st September, nevertheless for the football cup at the end of September ca.6000 football fans can enter! HU citizens returning from abroad are locked-down (quarantine) for 14 or 15 days, they only accept HU PCR Tests, nevertheless for the football fans Spanish or German tests will be also accepted. (she ranted on a bit) in HU one PCR test costs at least 150EUR per person. You need 2 tests to be relieved from the quarantine in about 5 days. If one lives in the countryside,it is bad luck, because you also need to pay another 150EUR so that they come to your house. As a conclusion, someone in the countryside is free after paying ca.450 EUR for the tests...Nowadays test centers are so busy,that they only take bookings 2 weeks ahead from now.
I read elsewhere that the PCR test might be just 84eur, not 150?