Proposed new set up:
3core 4mm SWA - earth is taken through the yellow wire - with the armour
sleeving bonded to the yellow wire at both ends.

I'd prefer to see 2 core SWA, with armour isolated at shed end, with shed TT
earthing by earth rod. I would also use 6mm minimum. 4mm is only just on the
limit for 20m, leaving no voltage drop left over for wiring within the shed,
if you design for the full 32A, which may be required in the future.

- 2.5mm T&E fed from a 16A mcb

Use a 20A MCB. That makes it one of the standard socket circuit types.

Shed lighting plus external light
- 1.25mm T&E fed from a 6A mcb

I've never seen 1.25mm T&E. Use 1mm or 1.5mm, whichever you have lying
about.

In-house connection is to a 32A mcb on a split CU and is protected by the
integral 30mA RCD in the CU (there are two split CUs in the house, this CU
only feeds shower and outside lights, so if it trips it's not a problem).

Feed it from the non-RCD side. In the event of an earth trip, you don't want
to have to return to the house to get the lights restored. There is no
requirement to RCD protect the SWA cable and the shed itself has its own RCD
protection.

6mm T&E is used to complete the circuit from the SWA to the CU at both
ends.

That sounds fine.

I realise that this means that the shed light will be lost if the RCD
trips in the shed. I could solve this by using a separate CU in the shed
for lighting only (I have a spare CU) or is this not permissible as the
light would still be lost if the 32A mcb tripped in the house CU?

If you want separate RCD protection for the lighting circuit, you have
several options, in descending order of desirability.

1. Use RCBOs in a non-split isolator incomer CU.
2. Use a split load with time delay 100mA RCD incomer and 30mA instant for
sockets.
3. Use two CUs, each with its own RCD.

An alternative would be to use the existing supply from the fused spur on
the ring main to feed a separate CU in the shed just for the lighting,
using a 5A fuse in the spur instead of the current 13A one. However, I
would have liked to have got rid of that cable altogether.

Yes, avoid this idea.

I assume that if a separate CU was used in the shed for the lighting, that
this would also require its own RCD?

Yes, especially with TT earthing.

Christian.