"Birmingham Road" isn't a secondary, and isn't signed as such at the north end, and nothing on OSSV or OS OM Local backs up that name.  I've left the name on the Charlecote end because someone presumably added that for a reason.
It is also I believe 60mph not 50mph (the A road is 50 here),
You could maybe argue for a tertiary for the northern part of it, but it's a bit of a stretch.  No road is _named_ after the cycleway here.