They wanted "red alert".

https://en.wikipedia.org/wiki/Red_Alert

This is just an idiom for denoting a high alert state.

No, "Red Alert" is called when there is an attack imminent, incoming weapons detected, enemies sighted.

So a macrophage on "red alert" would be reacting to an active infection or disease.

Sure, and this vaccine goads the macrophage into that state, putting it on "red alert", without there actually being an infection.

I suppose it is not worth debating a metaphor written by BBC reporters for the general public, without even reading the research.

But I was edified to learn that Dr Edward Jenner was a vaccine pioneer even without the honors of knighthood.

Perhaps "Defcon 02" would be better understood?

Notice that that Wikipedia page links to a disambiguation page which links to https://en.wikipedia.org/wiki/BIKINI_state which may be more familiar to people in the UK than the meaning you are thinking of