I was actually right (stopped clocks and all that):-
I suspect that at the sorting office they put them all in a big hamper and they get picked up just once per day, hence needing to do the test at the last possible moment. Given how screwed the system is however I doubt it'll make much difference.
I've still got a cough 15 days in and about 92% O2 saturation (which is a lot worse than it sounds). The night sweats (where you wake at any time of day convinced you're drowning) and occasional full body tremors are fun :(
I've just spoken to the Docs who put me back to 111, after 2 tries at the end of each which the robot thanked me for the call and hung up I tried the Docs again. I got more pushy with them this time and am waiting on a call back. Just Antibiotics would placate me at this time.