Genghis the Engineer
"(1) Is it not the case that automatic access to an aeroplane by a police offer must be when they are in uniform, and it doesn't apply to somebody in plainclothes?"
No. And it's not a right of entry to aircraft, that's more complicated, and dependent on country of registration, and what statute they are acting under.
As far as entry to airports is concerned, the right is for a designated Constable. I can't speak for all forces, just the Met Police, who are all designated constables. The power is regardless of uniform state.
However, the agreement between the BAA and Heathrow Police was (and I can't say if it still is) that only Heathrow Officers and SB are admitted to the Restricted Area. All others are only allowed in in the same way as a passenger, ie they are flying. If they need to speak to someone airside, then they go in with an Heathrow officer, and last time I took one in, which was a long time ago now, he was searched. The same applies to officers flying on duty, they are searched, except for armed protection officers.
The incident mentioned earlier, is without doubt abuse of the officers authority. If it happened, I'm suprised the local police didn't get called. It happened at LHR years ago, the officer concerned lost his job.