Well, this is my insight as a Hungarian moving to the UK & starting undergrad in the UK this year.
The University of Debrecen is a respectable institution in Hungary but it stops there, no one outside the country has ever heard of it. Anglia Ruskin is in the bottom tier of British universities but keep in mind that a British degree from any uni, good or bad, will always be recognized and respected all over the world. You can't compare a bad British uni to a good Hungarian one in terms of prestige. That's unfair, of course, because the quality of teaching etc at the Uni of Debrecen are probably much higher, but the reputation of a country is more important than the reputation of the institution you studied at if you plan to work abroad!
You also have to the consider other factors as well, Hungarians speak Hungarian. The younger population does speak English but on a much lower level than in other Western countries and about 50% of the people you would encounter couldn't speak a word of English to you so consider your social life as well.
I don't see why someone would choose to come to Hungary to study (or live or whatever), the institution issuing your degree will be a random no name one if you work outside Hungary, most people don't even know which continent Hungary is in! I understand that it's cheaper but that's probably not a good reason to choose one country/degree over another.
you can just not take this into consideration if you don't care, but this country just isn't a pleasant place to be right now. The economy is horrible, let me tell you that out of my 20 cousins, 11 have moved to Western countries to find work. I haven't seen half of the people in my apartment building because they're all working abroad. Half of my childhood friends have moved abroad as well, and the ones that are still here are waiting for opportunities to get out of here. Everyone is gone! There are no jobs, very low wages, the minimum wage is about 450 forint which is a little over a British pound. Yes, seriously.
The far right is also growing steadily, it is at a point now where it is an everyday thing and completely acceptable to vote for the 'Jobbik' party now which is the equivalent of the British BNP. A few years ago this would've been unimaginable. There's been a rise of racism (esp against Roma people), anti-semitism etc. This country is a social, economic and cultural wasteland at the moment because of the financial crisis. Which is why I'm moving out!
British degrees are regarded very highly in Hungary as well, most uni students in Hungary wish they could study in Britain but their English isn't good enough or they don't have the money for living costs so they stay in Hungary. People think I'm a God for going to uni in England. Employers would be lining up for me if I came back here after I finished my UK degree (but I'm not coming back).
You said the fees are low, but you have to remember that they are NOT low by Hungarian standards! It's very expensive by Hungarian standards and if you were to work in Hungary, paying back the loans on a uni degree on a Hungarian salary would take years.
It would also be hard for you to get a teaching job at an Eastern European university - courses taught in English are very scarce! It's very unlikely you could find a permanent job as a non-Hungarian speaker or non-local language speaker in an Eastern European country.
So anyways, I would not advise you to choose Hungary over the UK.