There are three key elements to making this type of thing work:
1) Moving to a country with a lower cost of living than the country you're being paid in.
2) Either having an employer who is totally OK with it (unlikely), or simply not telling them (can be quite easy depending on the job).
3) Making sure that the time difference between your "work" country and the country you're living in isn't so great that you're having to get up in the middle of the night or stay up really late.
In the majority of poorer countries, you can enter on a tourist visa and simply leave for a few days before your visa expires, then come back in and reset the clock. Considering the amount of annual vacation most jobs give you, this is relatively easy to do. As long as you don't overstay your visa and can provide proof that you have sufficient funds to sustain yourself, most border agents don't care. You could have course be unlucky and get one who decides to do a bit of digging but I don't know of anyone in Latin America / SE Asia who that's happened to.
Cards like Halifax Clarity, Revolut etc etc can be used for all your daily expenses, and you can open an account with a company like Global66 or Transferwise so you can pay your rent. If you end up getting into a relationship with someone out there, you can even buy a house / car etc and put it in their name until you get married, which will get you a visa anyway. If you don't, rent and ubers are cheap enough in a lot of places that it's a non-issue on a British salary.
In order to avoid the typical OCUK self-righteous pile-on, I should probably mention for those that might look at my location and make the obvious connection that I personally have done absolutely none of the above apart from the getting married bit, but I have helped a lot of people to do it and it's worked well for them.