Thanks everybody - very enlightening replies.
So:
Rushing to front of queue is a no no.
Best is to approach nearest attendant.
Airlines do assist in making a tight connection.
Its airlines responsibility to get you to your destination.
Airlines do hold up planes for arriving pax.
And best of all - if flying first - can expect to be ushered through to your seat. Now, if only I can use this to convince my wife that I should be travelling F