Don't forget that SMS is not an instant messenger service, whilst nowadays we are used to them arriving within minutes they can take up to 7 days. (There is a message validity setting in most phones which is usually set to maximum - this tells the message centre how long to keep trying to deliver).
Nowadays most messages arrive within 24hours , even at busy times, indeed some providers terms and conditions say they will make. every effort to deliver the message within 24 hours.
I suspect what's happening is that when on the underground, you get brief periods of service. All this 'on and off' means that the handset isn't properly registered on the network and messages get stuck for a while until the phone changes cell or a call is made. This seems quite common with some handsets but never seems to happen with others.