From the link above...
A different looking building next door may have been combined with the works, a sign above the door showing the name 'Barrowcliff Spinnings Ltd'. The 1943 Kelly's Directory of Birmingham & Suburbs (Brass Founders section) lists a business by the name of 'Walker & Woodward Ltd (cast hinges, stamped & bar work)' at the Legge Lane address. Baron R Walker's brass founding company manufactured a range of brass instruments, including spirit levels.
There are still signs and letters from Walker & Woodward in there. I think the two were separate companies. What's written on a wall or above a door outside can often be misleading.