I'd advise you to start applying now, because it will take a while to gather your documents and get them apostilled, and you need to leave yourself enough time to allow for international postage of your docs as well as visa processing.

For me, the entire process from application to visa collection took about four months (mostly because my documents took AGES). I don't know if the British government processing delays from the pandemic are still ongoing, but I'd assume that six months is enough to get everything processed in time.

- If you have a teaching license, it would definitely be in your best interests to look at teaching positions in International schools. They can pay double what a public school pays.
- If you have a Master's degree, look at universities. The pay is a bit lower, but your teaching hours will be about half of that in a public school ( the latter being 22 per week), and most offer 4 months of paid vacation per year.
- Avoid private academies if you have that option. Most work you ragged, and often the pay is pretty underwhelming. There are plenty of good ones out there, but usually those are only discovered after living in country for a while, and making connections etc.

I highly agree with the above!  As you are a qualified / licensed  teacher back in the UK, and offer 3 years of teaching experience, apply for the international schools! Those are the schools that offer US/ UK/ Canadian curriculum to children of expats and local Korean kids (whose parents can afford to pay the  20,000 USD per year or more). Working at an international school will not only give you double the pay, but also you will have similar responsibilities and authority as you did back in a UK classroom. However, when researching the international schools please be careful and make sure you go for the legit / accredited school s, which are able to legally provide you with the E-7 teaching visa. For example (Korean Kent Foreign school  (Seoul), Daegu International School, Korea International School (Jeju Campus).

With a masters, a university teaching position would be the next best job, not salary wise but due to the longer paid vacations.

I would also absolutely recommend not applying to the private academies called (Hakwons/ Hogowons), which mostly operate as independently owned businesses (think of pizza shops/ restaurants back home), and their main goal is to make as much profit for the school owner while paying as low as possible and overworking the teachers. (Also many other problems can occur while working for these academies... for example.. if you have a corrupt owner.. he might try to cheat you out of pay for months... and you cannot just quit and find a new place of employment because in Korea if you are on a E series visa ( E-2 for private academies) the employer owns your visa and therefore, owns you for the duration of your visa! 

Honestly, while the public schools (EPIK program) can be a bit better, I would avoid doing the EPIK program as it is more and more geared towards young university graduates taking a gap year to save some money for grad school, pay off some students debts ( which I doubt is even feasible with the rising cost of living and the low 2.1 (about 2,000 USD) starting wages (the EPIK teachers pay has not been updated in 15 years!!!) In 2005 EPIK teachers were making this amount when the minimum wage for local Koreans was about 2,000 ( $2.00 USD) an hour, and now the minimum wage in Korea is almost equal to that of a starting EPIK teacher. In EPIK you are not the main teacher, you are a "영어 원어민 보조 교사" A Native English Speaking Assistant Instructor" and you will have to work with co-teachers in the classroom.
You may get lucky and have amazing co-teachers, or some terrible ones.. You can be give a lot of freedom on your part of the lessons, or non at all and be reduced to a "tape recorder" which is when you just stand around and repeat some English words when asked by the Korean English teacher ( very very dull and boring). Also, there is no career advancement, as the salaries are maxed out after 5 years.
It is more of a luxurious paid internship for a young uni grad than a career.

If you want to make a career here, go the international school route, as you experience at an international school can be easily transferable back into the UK school if you choose to return in the future. 

I currently have a friend who works at the Daegu International school, and am acquainted with another who just left one in Seoul and can tell you that the above poster's information is a bit outdated.

International schools in Korea usually start at around 3,000,000 per month and can end up paying over 7,000,000 per month for those with the right qualifications and specializations.
Also, from they tend to get *very* nice accommodations and benefits.

Here's a current sample of benefits and salary from a typical school:
https://www.travelandteachrecruiting.com/international-school-korea/

Says 3 – 3.6 million won per month.  I am in this range.  I guess lower 3s when you take the housing out.   Only 3 weeks holidays?  I am sure true international schools in other countries will do better than this. 

As the job posting clearly states, your choice of housing or a housing subsidy is on top of that. And 3-3.6 is *starting*.

Also, as I already mentioned, I know several people who earn twice that because they have in-demand specializations. This is miles and miles above most other ESL positions in Korea.