When people talk about depth of skirting they normally mean height. I have a feeling you mean thickness. Easy enough job to do, though - get the local timber yard to do you some 30mm wide rips of 12mm MDF and glue them to the back of your 18mm skirting top and bottom*, if your skirting is MDF. If your skirting is softwood, purchase some ready-machined 12mm thick planed softwood stop lath and glue that along the top and bottom* edges at the back. Use a block plane or hand plane to plane in the top edges of the skirtings nice and flush.
* If you still have the softwood grounds for the bottom of the skirting attached to the wall, just add the top filler piece.
This is a fairly standard work around - just make sure your architraves will accommodate it.
BTW this is not at all bizarre - it was common in larger Victorian and Edwardian houses for skirtings like that to be made up on site and fitted onto softwood timber grounds at the foot of the walls. You may come across anything from 2- to 5-piece skirting made-up this way. I've replaced a lot of this stuff over the years and even built matching 5-part 14in high boxing to hide radiator pipes in one listed building. The top "dado" section isn't dado rail, it's more like a sort of bolection moulding or a picture frame moulding with a big rebate at the front, but either way I've never seen an off-the-shelf moulding quite like that, so I think bespoke would be the only way match it. But would you want to?