Immigration doesn't extend visas. Immigration extend the time you were allowed to stay upon arrival. It's called "extension of stay" and works perfectly with visa exemption entries.
I am in the same situation. My worry is if immigration will accept the seasoning money as I understood that money should be coming from abroad for the first extension.
In other words, you want an extension to stay in Thailand with a wife... who will not be in Thailand. That's how immigration will understand your request.
It's not a matter of citizenship but residency. If you're resident in the UK (whatever your citizenship is) you can use your driving license abroad during holidays (international standard is 90 days). If you become resident of another country, you're supposed to exchange your British licence with a local one and you can use it in the UK if you come for vacations. The good thing with Thailand is that they don't keep your British licence like they do in many county (ie Canada, Australia, USA, all Europe) when they give you the Thai one.
According to international agreements, you should get a driving licence of the country where you live. That's why you can't get a British one with a foreign address.
it happened to me once, the boss was at a meeting in Bangkok and couldn't sign the extension stamp. They stamped under consideration 15 days. He came back the following day and I got the 1-year extension.