Excellent end result Brian - mission accomplished!
As to B&Q plywood, most plywood sold by DIY stores is 'construction grade' plywood - not 'furniture grade' which is known as 'birch through and through'. In other words, each ply is birch and of the same thickness. B&Q do sell 'birch through and through', but only in 8' x 4' sheets. Construction grade plywood has a reasonably presentable veneer each side, (usually a light pink/red colour), but thicker and softer inferior coarse-grained plies between the facing veneers.
There are companies who will cut plywood to size - this one for example, will cut softwood ply, marine ply or birch ply, but when we're renovating old radio cabinets, if the radio is of little value, costs must be a consideration.
If you put your dimensions, thickness and type of ply into the price calculator you get an instant quote:
https://www.woodsheets.com/plywood-s...irch%20Plywood
At the gallery at the link below, among the rocking horse pictures at the top there is one of an unpainted rocking horse made from birch through and through plywood, which highlights the muscular contours of the horse:
https://www.rockinghorse.co.uk/hand-carved-horses.html
I've attached a (not very clear) picture showing the two types of plywood.
Hope that's of interest and relevance.