The letters b and q stands for Block and Quayle. 

Block and Quayle

B&Q PLC is a British international DIY and home improvement retailing firm. Its headquarters is located in Eastleigh, United Kingdom. 

Block & Quayle was founded by Richard Block and David Quayle in 1969. It provides over 40,000 products, over 300 physical stores and online outlets. The business also has a few locations in Ireland.