The BOE would not be paying any commission offered on an exchange at a bureau de change. They are no doubt funding the post office for their service to exchange notes.

As I suggested upthread and added by others a bureau de change may take pity on a potential customer wishing to exchange withdrawn BOE notes. They do not have to do so. If they do so they will need to bank the notes concerned (rather than recycle them out to the next customer who wants sterling), not a big deal for them, but it's still something that they have to do.

No one would force a holder of withdrawn bank notes to use a bureau de change to exchange withdrawn sterling bank notes, nor would the bureau be compelled to offer such a service. But it could, and if so would be offered as a convenience to the customer and my guess is that would not be unreasonable for the bureau de change to levy a modest fee for the convenience of offering the service.

A customer can then weigh up the cost of the service being offered against the time and cost of going to the BOE or a designated crown post office which may not be convenient and will probably involve more time queueing to get the service for no commissionable cost to them.