Thanks for that link Simon, not one I had come across.
I understand their premise, and agree with some of the points made in that article, however their argument is made purely from the point of view of preventing backdrafting into the room, as this is the basis for the legal argument for installing additional air.
They say that adding external air is ineffective at preventing backdrafting (due to external pressure difference etc...) which I can understand. However, they don't really address the other possible benefits of adding external combustion air, relative to the whole living space.
When air is removed from a dwelling by any means it must be replaced by air infiltration. By controlling where the air infiltrates you gain more control over the air circulation and flow of heat within your home.
For example, you may envisage a situation where your stove keeps one room of your home hot, the adjacent rooms warm but further rooms are cold. If air is infiltrating your home in those further rooms, to make up air to your stove, it makes it substantially more difficult for natural convection to circulate warm air to those distant rooms - the air faces an uphill struggle against the flow of cold air into the building.
If you deliberately place an air inlet into the building adjacent to the stove you effectively provided a much shorter, direct path for that cold air to reach the stove. The cold air that feeds the stove isn't being dragged from the furthest corners of your home before it gets there.
What this means in practice is that the cold air that used to flow along the floor of your home, chilling ankles, will be dramatically reduced because you have chosen where it flows.
My experience of using an airbrick to supply external air comes from using a gas stove in an old rental property. We were required by law to have an air brick fitted and the only place it could go was on the opposite side of the room. Fitting this air brick dramatically changed the air flow in the whole building.
Previously the majority of the air infiltration had been from upstairs (leaky loft access and a small window vent in the bathroom) - cold air flowed down the stairs, through the hall and across the sitting room floor before reaching the fire. After the airbrick was installed air flowed directly from the brick to the gas fireplace, across the living room floor.
The upstairs rooms and hallway were noticeably warmer as a result, although the draft across the sitting room was inconvenient.
A more ideal location for the airbrick would have been immediately adjacent to the fireplace so cold air had a limited path, without crossing the living space. The configuration you describe sounds like it could achieve that end.
I suggest you investigate the airflows within your home before deciding what to do. It is fairly easy to figure out where air is flowing and infiltrating - get your stove burning nicely and open up the air supply fully. Light an incense stick and observe which way the smoke flows, especially in passage ways/doorways. Hold the incense at various heights so you can get a feel for airflow into and out of a room. If you find a particularly "leaky" room you could try draft proofing and if you find substantial flows of cold air through passageways you could try adding the air brick.
I hope that is of some help!
Mike