What derating table do I use for multicore armoured thermosetting cable in insulation.

Not too sure what you are describing. It looks like you want a 60A distribution circuit and have an existing 16mm2 T/E in place but installed as reference method 100 thereby giving a table 4D5 current carrying capacity of 57A. 
I can’t imagine a constant 60A demand in domestic circumstances but if you want to be squeaky compliant then you are correct to seek an alternative, which might include a more detailed consideration of the maths.

Personally, all other things being ok, it wouldn’t cause me a second thought to leave the existing arrangement in place. I am not even sure if I would write it up as a deviation on the EIC!

Not too sure what you are describing. It looks like you want a 60A distribution circuit and have an existing 16mm2 T/E in place but installed as reference method 100 thereby giving a table 4D5 current carrying capacity of 57A. 
I can’t imagine a constant 60A demand in domestic circumstances but if you want to be squeaky compliant then you are correct to seek an alternative, which might include a more detailed consideration of the maths.

Personally, all other things being ok, it wouldn’t cause me a second thought to leave the existing arrangement in place. I am not even sure if I would write it up as a deviation on the EIC!

My main concern is a non armoured cable, without 30mA rcd protection running through the fabric of a building. If I put a 30mA RCD on the submain most of the house circuits are protected by a single RCD. If I wasn't making changes I would probably just code with a C3; but I am changing the CU on the supply and load side, therefore believe the circuit needs to comply with current regulations.

I am changing the CU on the supply and load side, therefore believe the circuit needs to comply with current regulations.

I'm not sure that's actually a requirement - to take that demand literally would mean replacing or re-marking at all positions all red/black wiring with brown/blue when replacing a CU - as red/black doesn't comply with current regs, or re-clipping cables that are only held up with plastic clips or plastic trunking, or 101 other changes the regs have brought in over the years. Certainly you shouldn't do anything that would reduce the safety of the existing (e.g. replacing a 15A fuse with a 16A MCB where Zs was good enough only for the previously acceptable 5s disconnection times), and upgrades where sensible/affordable/agreeable-to-the-customer are never to be discouraged, but to my mind it's only your new work (and the direct consequences of your changes) that needs to comply, not parts of the exiting installation that happen to abut it. Certainly draw the inadequacy to the customer's attention - that's what the 'Comments on exiting installation' box on the cert is for.

   - Andy.