I have certainly seen 2mins notice at Marylebone in the past.
Due to disruption, one platform had two services in it, with the one at the country end due to depart 2min ahead of the one at the buffers, so the latter was only unlocked and displayed on the boards once the former had departed.
Chiltern apparently have a policy of refusing to advertise the rear train under these circumstances, even in exceptional cases like this, to stop people boarding the wrong one.
The headway at Marylebone is 3 minutes, so you won't find a booked 2 minute separation in the timetable; but let's not split hairs over a minute as the same predicament can occur with 3 minutes notice - so let's assume the train on top leaves at xx.00 and the next train's scheduled departure time is xx.02 - leaving a less than optimum time for boarding and dispatch to take place.
There is no such policy, but it's not common practice to advertise two trains on the same platform for the reason you mention. In the last few years there have been practical solutions implemented to try and ease the issues of tight boarding times, such as the introduction of boarding area A initially and subsequently boarding area B. More recently the implementation of 'dual-boarding' at Marylebone allowed certain services to be boarded twice whilst occupying one platform under certain circumstances, which were basically ensuring that there were means to ensure customers who were on the platform were able to get assistance for getting on the right train. Those have no doubt helped with information and customer flow around the station. In disruption the demand for customer assistance on the concourse with the staff that are available to do so means that the practicality of boarding two trains at once in the same platform is reduced.
Generally if the train is on the buffer stops of Platforms 1-3 then the ideal time to posting and removing the train from the boards is less than if the train is on Platforms 4-6 (on the buffer stops, or worse on the top of Platforms 5 & 6). Adding additional complications into the mix such as posting a busy train on Platform 4 and the same time as an arrival of a busy train on Platform 5 or 6 should be considered too, especially then if there is a train to be dispatched on Platform 3 first. There are temporary fences still in place to help segregation between Platform 3 and the cycle rack/through route to Platforms 4-6. So, it is sometimes helpful to deliberately not post a train until the customer flow has cleared - or post the train and temporarily take it off the board until the customer flow has cleared. There are lots of other methods of managing customer flow, but I do hope that provides a little more information or insight than might immediately be obvious.
There
are times when trains
are held and delayed on departure, with incoming services either being held outside or delayed waiting the same platform. However there must be a cut-off and that is usually down to communication with the dispatch staff, i.e., are there people still coming down the platform for the train. Is it perfect, no. Is there scope to improve, yes. A lot of this is down to decision making by the staff employed to do just that rather than decision making by machine, and they are held to account by everybody including themselves.
Marylebone also had a reputation for not putting it up at all by departure time in such situations, and the train leaving on time, empty.
It did? Must have passed me by!
