Abroad is fairly general!
I guess you can do it two ways: have a look within the UK for courses which interest you, and then try to find comparable courses elsewhere. Or (the way I'd do it/am doing) is to pick a country/area you'd realistically like to live in for a year or two at least, and then look at the different university options within that country, decide if the university system is for you, then look at different courses. Moving somewhere abroad for a prolonged period of time is very different to choosing a holiday destination, so somewhere which is great to go as a tourist might be horrible to live in perminantly, whereas somewhere you'd never dream of going on holiday might make the perfect university location. You have to filter in things such as ease of getting back to the UK and the cost, the cost of living, residency and immigration (not so much of an issue in the EU), banking and funding, language etc.
For me, funding, language of instruction and international reputation are the most important factors to consider. For example, if you study within the EU you will only pay the same amount as students from country X pay, meaning if you go to a country where university tuition (including masters) is free, then you will get your education for free. This is the case in Finland, for example. Then you need to consider language, as are you comfortable in being taught in a language other than English? if not, then consider countries where language is used - in Scandinavia you can generally do an entire degree in English, but you will probably have to take a minimum amount of credits in language classes to learn your host countrys language(s). If you're not up for language learning in an academic context, then you'd need to look at native English speaking countries. Finally, reputation is a factor I am considering too, but you may not be bothered about this.
I don't think studying outside of the UK instantly means it is a 2 year course as it depends on the university. I'm currently an erasmus student in Finland, and thus have knowledge of the Finnish education system as well as most European ones as I have friends from all over the EU. One thing I have realised is that in many EU countries EVERYBODY studies for a Masters, there isn't really such a concept of graduating with a bachelors and then deciding whether or not to do a masters, as there is in the UK. In most countries you start university to do a 5 year course and get a masters at the end of it, and after 3 years you'd get very little recognition for your time in education unlike the UK. This means your masters course may not be as 'dedicated' as it might be in the UK, because everyone is still there and it is basically still undergrad and part of the whole university experience. Thus, you don't just have the people who are willing to pay £6000 because they are really really interested in the subject, as you tend to in the UK. Even though I am only in my 3rd year of a 4 year undergrad degree I have been taking masters level courses in Finland because they were the most interesting, and to be honest, I haven't found the standard of work challenging at all. It certainly isn't any harder than the work I did in first and second year at Edinburgh, and this is supposed to be something students undertake after at least 4 years at university, not two, which is something you might want to consider in terms of academic work/value of doing the masters.
I hope some of that can be of use to you, I have only started exploring my options this year because I feel the world (well, Europe) has opened up to me since being an erasmus student because I can find out very detailed stuff about the education system anywhere in Europe. I don't know anything about outwith the EU though, so someone else might be able to help you, but at least this is a starting point.