They are separate entities, they have been since Royal Mail was privatised. Post Office Limited runs the offices where postal and other services are provided/sold, including those of Royal Mail. Royal Mail Limited runs the postal service which moves and delivers the letters and parcels.
I wouldn't say having a shop front is a conflict of interest and postal agents exist as is so I only see it as removing a piece of a public utility in favour of privatisation.
Generally speaking, privatising public infrastrucure causes issues and added expense for consumers, less stable jobs and removes the benefit of the public investment.