does AUK insurance cover us?
No. It's only valid during AUK events in the UK - and in any case it's insurance of last resort, so will only come into play if you have no other insurance that covers you.
Not sure about BC, but you may be covered for 3rd party liability under your home contents insurance or under any travel insurance policy you have. Cover while cycling tends to be pretty well hedged with caveats though: when I've looked at the detail of previous travel policies, they've excluded cover where cycling was the main purpose of the trip.
(I've been shilling for
Pedalcover in Peter's thread on home insurance, so I might as well continue that here: they're explicit on the website about providing £2m of liability cover with home and travel insurance, and including cover during events. We've got our home insurance with them, and I'll be tempted to go with them next time we renew our travel insurance, as long as the quote is sensible.)