Cycling in and around Birmingham England
Cycles are allowed
As the blue sign at the start of the road states Buses and Bicycle then I would imagine YES you are allowed BUT I understand the confusion with the No Entry sign just after. It appears its a possibility that the No Entry signs were the original signs and the blue signs were added later as an after thought.
If anyone complains to you going through here tell them the blue sign at the start gives you the right of way. Bassically its like: a Bicycle Lane sign with a No Entry sign just inches pas the 1st sign. So cycles have rights to continue.
I wrote a Push Bikes report with several photos about the poor and inconsistent cycling routes to QEBH and sent to the estate manager but no response. Perhaps time to chase!
This is one inconsistency others are the very poor cycle route using the road to the main hospital entrance (and all the bike stands). Vincent drive crossings are dangerous and exiting at the hospital is poor. Elsewhere the cycle path is shared with all the bus stops! And the most obvious route from the station demands Cyclists Dismount.