Depending where you live overseas and what currency you're being paid in, you may need to earn considerably less than that to live comfortably (or, in some areas, considerably more). If you're living in a low cost of living country being paid in e.g. USD, GBP, etc and taking advantage of a favourable exchange rate your money goes a lot further so you can earn less and live like you're earning more equivalently.
Whether it's realistic is hard to say. Note that most other countries have defined training programmes to become teachers and potentially teaching assistants so you may not qualify by virtue of any course you complete in the UK which will be ultimately designed to qualify you to work in the UK education system. You may therefore be limited to only working as a tutor there or in private educational providers who may not need to employ staff with the same qualifications as a state education system does.
Note just doing a qualification in TEFL alone is probably not enough, you'd most likely need to fluently speak the language of that country as well so as to support students in learning English who can't speak it well already...especially for younger students who are unlikely to have high levels of fluency in English if you're not living in an Anglophone country unless they come from a bilingual family.
Finally also consider how many hours you will be able to work. The only people I know who worked as teaching assistants were not able to be offered full time hours because there simply weren't enough hours available for them so they did it part-time while working part-time in other roles as well. This may of course vary but do keep it in mind - hourly/yearly pro rata wage is only one factor, you need to consider if the job is actually being offered full time with guaranteed hours. For things like tutoring you won't have guaranteed hours, and for teaching assistant roles you may need to take up multiple posts at different schools to "make up to" full time equivalent work. Or combine the two (but as noted you may end up with no tutoring hours sometimes - you need a plan for how to make ends meet in those cases).
It may well be possible but I think there are a lot of details you need to work through. I think 3k a month post tax is unrealistic though (granted as above - you may not need to earn that much in another country to live a similar lifestyle to a lifestyle in the UK on that much). To take home 3k a month after taxes etc, you'd need to actually be earning £47k+ per year. I seriously doubt that is achievable in this case. Most graduate salaries aren't that high. In fact that's 10k per year more than the UK median salary (~£37k). So no matter what I think you do need to manage expectations around income regardless.