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Yesterday as an example, the train was delayed by 40 minutes at Derby, but by reaching its destination this had snowballed to 58 minutes.
This happens the same way when the delay is just a few minutes. Once the train loses its path, it loses its priority and trains running on-time will be put ahead of it.
A 3 minute delay waiting for passengers could mean further down the line a slow all-stations train that is running on time gets put in front, meaning the train can lose half an hour or more. All those delay minutes would be attributed to the dispatcher you spoke to who decided off his own authority to hold the train.
When control agree to hold a train - they will have looked at recovery minutes in the schedule and work out where the train will be back on time, and they also specify a maximum amount of minutes to hold the train by.
You also need to consider that many people on the train will have tight connections/missed connections as a result of them waiting for you and your wife.
It works the same way as if your flight is delayed due to awaiting passengers transferring from an arrival, quite often you will hear the pilots tell you they have lost their departure slot. This can then lead to further delays at the destination, as missing their arrival slot means that ground staff are not available for things like baggage handling and steps. This is why low cost airlines do not sell any through-tickets.