But METV is a TOURIST visa. That means it's for tourists. Whether you have a visa or not, immigration is the one who decides if you get to enter Thailand. And if you just spent a potential 9 months in Thailand and try to return as a tourist 3 months later, they're likely to take a dim view.
As long as you paid already, then it should be within a week. London is usually quite fast. But sometimes if they have a slowdown they prioritize processing applications based on departure date, so if you put a date far away, they would not prioritize your application and it could take longer.