Hughes joined Asda as head of public affairs in 2003, having previously held public affairs roles at Tesco and Edelman.
A spokesman for the firm said: 'We've been discussing with Bernard the balance of resources and skills we need between London and the rest of the UK to respond strategically and effectively to the new challenges we face. As a result ... Bernard has decided to leave to pursue new opportunities.'
Hughes has already accepted a role as chair of UK Regeneration's Big Society task force.
Asda retains TLG for public affairs in the UK.