I traded my old car in at a garage on 18th August. However I just realised another monthly direct debit left my account on 2nd September for the tax for that car.

I didnt cancel the direct debit as the Government website says there is no need to do so as when they receive the new owners slip-they will do so.

Leads me to think the garage maybe didnt send it off very quickly but surely its in their interest to do so, so they can sell the car on?

They haven't transferred it and is currently the getaway car in a bank job. Expect to be arrested at gunpoint by 'the Feds' or maybe even tasered at which point you'll shit yourself or die. Possibly both.

Was nice knowing you Grave.