There we were in the vaulted tunnel running,
You in your going-away coat speeding ahead
And me, me then like a fleet god gaining
Upon you before you turned to a reed
The “we” is Heaney and his new wife. The atmosphere is that of a dream or fantasy. 
 The “vaulted tunnel” refers to the underground, traffic-free linking pedestrian underpass from South Kensington tube station, along the length of Exhibition Road and emerging close to the Royal Albert Hall where the Proms are held. 
 The “tube” is the underground train system in London. 
 
 The idea of a “vaulted tunnel” is dream-like or nightmarish even, somewhere mysterious and without end. 

The Underground