From what I can decipher from Realtime Trains, the 0649 Wolverhampton to Walsall is being split from the December timetable change into separate trains.
The Wolverhampton section will now run through from Shrewsbury as the 0558 Shrewsbury to Birmingham New Street, which goes on to form the 0726 Birmingham New Street to Shrewsbury (so presumably will be formed of a 170), whilst the Walsall section runs through from Crewe as the 0620 Crewe to Walsall (booked a 350), which returns as the 0801 Walsall to Birmingham New Street, then joins the 0811 Coventry to Birmingham New Street to form the 0854 Birmingham New Street to London Euston.
EDIT: The 0649 Wolverhampton to Walsall doesn't exist in the current timetable, but these are the arrangements in the new timetable...
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Having looked at the new timetable, it appears the 0619 Wolverhampton to Walsall had first class and no longer does - this is what now happens with it...
The 0619 Wolverhampton to Walsall terminates at Birmingham New Street, returning as the 0708 Birmingham New Street to Wolverhampton (which used to be formed of an ECS working from Wolverhampton). This diagram is a Class 323.
The 0647 Birmingham New Street to Walsall is still a Class 350, formed from the 0617 Birmingham International to Birmingham New Street (which appears to stable in Birmingham International station overnight). It then goes on to form the 0730 Walsall to Liverpool Lime Street as it does today.
