Is the interconnecting cable between outdoor and indoor AC units classed as a control cable or power cable?

Could be either ... or both.

It's certainly part of 'machinery' as defined in the Supply of Machinery (Safety) Regulations, and therefore not completely in the scope of BS 7671 ...

• I believe it should be in scope of BS7671, as someone needs to certify it on install as compliant, and any cables used for Power should comply with BS or harmonised standards

Not sure about that - there is no reason a competent person cannot install to the relevant machinery standard by following well written maker's instructions, which may need you to do things that are not be as simple as BS7671.
Actually we already see this with things like heating controller wiring and alarms and so on, where '7671 does not really cover the situation. As a very noddy example how would you test a Honeywell Y plan boiler installation to BS7671 ? Concepts like Zs go out of the window with 3 way valves stalled in mid position with diodes across micro-switches.Usually, as the boiler is considered an appliance, so you don't test the installation components, just the whole thing.

David Alcock said:

I believe it should be in scope of BS7671, as someone needs to certify it on install as compliant

Compliant with what? I agree with Graham, there seems little doubt that the cable is connecting two parts of a machine.

Let's suppose that your friendly local sparks installs a new circuit which terminates in an isolator. He (or she) notifies the new circuit to building control. That is BS 7671 sorted.

Householder then pops down to Screwfix and wires in the ACU. There may be a requirement to notify under another part of the building regulations, but that is not what we are talking about here.

David Alcock said:

I believe it should be in scope of BS7671, as someone needs to certify it on install as compliant

Compliant with what? I agree with Graham, there seems little doubt that the cable is connecting two parts of a machine.

Let's suppose that your friendly local sparks installs a new circuit which terminates in an isolator. He (or she) notifies the new circuit to building control. That is BS 7671 sorted.

Householder then pops down to Screwfix and wires in the ACU. There may be a requirement to notify under another part of the building regulations, but that is not what we are talking about here.