I would personally be happy with the TV just on the wall, however, if you wanted to 'flush' it in I would think the way to go would be to bring the wall out, creating an alcove that can be either plastered or lined with timber, similar to a window reveal.

A stud wall such as this would cost a few hundred quid I guess, and the lecky side of it around £100 or less - I would expect it is just adding a couple double sockets.  The cables from the TV could be dropped in behind the false wall to your AV kit, including the TV mains lead.  Having the bottom cill of the reveal removeable would facilitate this, or drop a length of gutter down pipe in.

Taking a foot or so off a room to flush your AV kit in seems excessive though, unless the room is huge.

You would want to consider ventilation for the AV kit - sky+ boxes in particular do not like the heat of cupboards - they generate heat themself and the cupboards get very hot, leading to the boxes locking up etc.  Make sure there are ventilation holes somewhere in the final design of your cupboard.

The reveal for the TV may also need consideration with regard heat - What does the manual on your TV say with regard distance from walls and ceilings?  Usually they state it must be no closer than 100mm or so from the ceiling or walls, which in this case would be the insides of your reveal.

Adding a false wall like this does not need any planning control, and is not likely to require building control either.