Tends to be 30 seconds in the North, don’t really see any deviation.
LNER can and do lock their doors more than 30 seconds before the advertised departure, regardless of what the policy is.
At stations further south, an extreme example is Euston where you can be denied boarding 2 minutes prior to departure and trains can depart a minute or more early.
Whether or not there have been posters at New Street for months or minutes, it is very customer-hostile that every single major station appears to be setting its own rules. 40 seconds at New Street, 30 seconds there, a minute somewhere else, and so on (and that's before we get onto Kings Cross's new "trains removed from screens 3 minutes before departure"). How on earth is the occasional traveller meant to know this?
Indeed; in sensible countries that really know how to run railways (Switzerland, Japan), the final boarding time is the advertised time. The idea that it depends on whether it's Euston, Birmingham New Street, or Sandwell & Dudley, is nonsensical.
However, there is no-one with any powers that actually cares about this sort of thing; there is no effective regulator, watchdog or ombudsman to resolve this.
The current practice of custom times that are unfavourable to customers is also robustly defended by some within the industry, and there really isn't anything to debate on the topic that hasn't been debated before.
If anyone has anything new to bring to the discussion, feel free to do so, but there is no point having the same debate again and again. Neither side is going to budge.