More that their Commonwealth status means Britain would intervene, which means the US probably would too, and at that point it's about 90% of the way to being a NATO action even if no-one else joins.
Commonwealth doesn't mean anything. It's a very loose association of counties with shared history not a defence pact.
Even so, I think Britain refusing to aid a Commonwealth member under credible foreign military threat would be pretty surprising. More so with Australia and New Zealand especially, since they share a head of state. Besides, ANZUS and Five Power exist to pull the US and Britain, respectively, into a conflict that threatens those states.
There's no chance the UK goes to war with China over anything unless the US does so first. It won't be the other way around, Commonwealth or not.
How would the North Atlantic avoid that charge?
Why is the North Atlantic even aligned in the first place?
So as not to slop over its brims. It has been found that having the body of water exactly aligned with its containing basin at all times is the optimal solution, especially for residents of coastal areas.