How to 'break' this magic link?

[Ajax Bay]

6 (rear cogs). Not sure why I have a 'narrow' chain... fitted by a bike shop

The chain is CN HG 40 which is the right width for a 6 speed (and 7 and 8).

the chain [has] started slipping under power

I'd say that if the chain is slipping then it and the sprockets are knackered. No amount of cleaning will fix that. New chain and cassette/freewheel I think.

Agree with @Vantage - if it's slipping under power (probably only on some of the sprockets) you've let it go too far and you need to replace both chain and block.
Wiggle at sub £4! Maybe KMC would be better. A new 6 speed freewheel will be a bit more (?£7).