Just taxed mine at the post office, didn't need to show insurance, only MOT. Black MY2013 SD4 GS Auto, Wood Company Armrest, Freel2 sticker.
Gone MY2010 Freelander 2 Manual TD4.e S, Alaska White.

When you check online it may well be that you are not checking the 'actual' database but a different one that shows the vehicle status, for data protection etc If this is the case then maybe that explains the lag?

Quite right - as we found out a few weeks ago in a previous thread (might even have been this one!), an insurance check no longer forms part of the process to tax a vehicle unless you live in Northern Ireland.

I suspect very much that the database that the DVLA web server connects to is not a live one. I suspect, like the PNC, it receives an update every few days and so will never be "live".

However, should a police officer need to check the status of a vehicle by the roadside, they would contact the DVLA direct who would obviously have access to the live data. As such, a vehicle that was taxed a few minutes ago would trip an ANPR but on further check would come up as "taxed".

I would imagine, on a practical level, that if a vehicle ONLY pinged an ANPR for "no tax", the officer would check with DVLA direct before stopping the vehicle. This would mean you would never be stopped at all......