In my experience- volume will be calculated based on external measurements, and the Council will measure from your drawings. The volume check is one of the basic checks they will tick off, long with the 200mm set back from the eaves, side facing windows being obscured and fixed shut up to 1.7m, materials proposed matching the main house (e.g. clad in tiles to match the main roof, windows to match those of the main house etc.) etc.
If your drawings measure over 50m3 externally you are likely to get a refused LDC.
However we all know LDC are not requirements, and they are paper exercises and the drawings are often not complied with on site, so really is down to you to decide whether you want to build something which needs planning permission or not. And if you do need permission, whether you apply for permission or wing it is your call.
LDCs are a red herring- it's about whether it needs permission or not.
Planning Jungle summarises all appeal decisions and I imagine this issue is covered by PJ, but you need someone with a subscription to PJ to take the time to go through it.