Doors regularly lock 30 before departure time across a lot of the Southern network. I always assumed it applied across a lot of the London & South-east Network. It's common for the public arrival/departure time to be exactly the same as the working departure time with the working arrival being a minute earlier, so if the train is going to depart on time according to the working timetable they need to be shutting the doors early.It's important to remember that this whole locking doors before departure thing is mostly a thing at major stations where trains have dwells, and at termini. Most intermediate stations the arrival time and departure time are the same, so the situation does not come up.
The kind of people who will complain about the train leaving 45 seconds late and arriving on time at the next station/the destination, will find something to complain about regardless. The departure time should be the last time at which a passenger can join the train (in my view at least). At most stations, that is what is currently in the timetable. At stations with the whole "doors lock X minutes before departure", that is the departure time minus X. At Euston, that will be the time they close the barrier (if they insist on continuing that nonsense). People may well learn that in some cases the train departs 1 minute late some (or even most) of the time, but no reasonable person could argue that they were wronged for a train departing at the advertised time. The UK is an outlier with regards to locking doors and barriers before the time shown in the public-facing timetable (which may differ from the working timetable).
You also want all the buffer you can in case of a slower-to-deal-with passenger at a later stop, so if you're allowed to shut the doors early and get shifting then there is always a temptation to do so.