Hi
I agree the wiring looks like a complete mess.
I did some tests
On the NEST (on / off refers to the status in app)
Heat Off HW off
1,2,4 and 5 are live
Heating on HW off
2,3,4 and 5 are live
Heating off HW on*
1,2,5,6 are live
Both on
2,3,5,6 are live
Above seems to suggest NEST...