Yes, they do. Why wouldn't they? If they wouldn't use it AFB would have not been installed on the rolling stock. It is a massive aid in driving the train and also adds safety to the railway. They won't use it in certain situations where it is either forbidden or handier to drive manually, but in general, they use it when possible.
I only know one reason when train drivers don't use the AFB and that is when they are transporting liquid cargo such as oil or gasoline.
Then why don't UK drivers use speed set? I know it's a bit different to AFB but it helps with driving
I'm pretty certain that most drivers use AFB in routes with steep gradients such as MSB. And most use it with LZB too. However at the end of the day, it comes down to the preference of the driver.