OK then, as drawn above, 1-4 are all power conductors by your definition - agreed ?
I assume that you're talking about your drawing (since mine had 1-3 and 1-8) - in which case, yes, I agree.
What if the boiler gets replaced, and the new one is a 3 wire one where the demand (conductor 4) is only a signal and the boiler takes it's power from the permanent live ? .... Surely now you are adamant that all four of 1-4 are now control wires because they don't carry the load current of the boiler.
Yep, that's what 'my' convention would say (in that simple situation). It perhaps becomes clearer if one thinks of a situation in which all your 1-4 (timeswitch and 3 stats), hence also the signal line to the boiler, were operating at ELV. In that situation I doubt that anyone would deny that all of that was a 'control ciciruit', separate from the LV "power circuit" connected to the boiler (which would take the full load current when the boiler was 'on').
But you are equally adamant that 1-3 are power because they carry the pump current. Yup, totally black and white
As I wrote ....
....The example you give is slightly complicated by the fact that there are two loads but if one forgets the pump then I would say that what you call 1, 2, 3 and 4 are all parts of one circuit (not four circuits) - which is simply a load supplied with power via four 'switching devices'.
... so, yes, you have managed to come up with an area which is 'grey', rather than black and white, since, with the pump per your drawings, it is a 'dual-purpose circuit. That is, of course, only possible because the control circuitry is LV, so one can ('conveniently') use what is a control circuit for the boiler as a power circuit for a pump. If, as above, the control circuitry was ELV, one would have to incorporate relays/contactors to operate the pump (which is the situation I have in my house) - in which case the situation (per my definitions) becomes 'black and white' again.
As for Table 51 of BS7671, I leave it to you to form a view as to what colours are permitted in a dual-purpose (power+signal/control) circuit, since no such animal exists in the Table. It's similar to the situation (with a different BS7671 Table!) when one has a 6A or 10A 'dual purpose' circuit supplying a number of lights and also (compliantly, despite some views expressed here!) one or more BS1363 sockets. Does such a dual-purpose circuit qualify as a 'lighting' or a 'power' one - and hence is the minimum cable CSA 1mm² or 1.5mm²? Your guess is as good as mine (in both situations).
Kind Regards, John