The normal route for family migration requires you to make at least £18,600 for the past 6 months if it's just your spouse that you're sponsoring. If there are children, you'll have to make more. In addition to the monetary requirements there are other hoops to jump through.
Now most TEFL teachers aren't rich, so there is a loophole.
The Surinder Singh case changed British law and allows people living abroad a little more leeway when applying for a spousal / partner visa. Instead of having to fulfill British laws to get a visa, you have to fulfill EU laws. This basically means that the British spouse / partner doesn't have to meet income requirements in order for their spouse or partner to get a partner / spousal visa. Eur-Lex has more info about the official ruling.
This is great news for British TEFL teachers who may not earn enough TEFLing where they are now. They simply have to establish themselves in another EEA (EU plus Iceland, Liechtenstein and Norway) for six months and then they can apply.
If you have at least £64,000 in a British bank or an equal amount in investments for at least 6 months. You also have to prove that this money is yours and not a loan.
If your spouse is from an English-speaking country and/or from a 1st world country, your application isn't looked upon with the same suspicion as it would be if your spouse was from a place where moving to the UK would be considered a financial incentive.
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