Geoffrey Chaucer’s Canterbury Tales follows an eclectic bunch of pilgrims on route to Canterbury Cathedral in the fourteenth century and recounts the tales they tell on the way. 
Nowadays Canterbury is known as the spiritual capital of – well, if not of England, then of the Anglican Church, and in Chaucer’s day was the most important Catholic cathedral in England, but that is not why the pilgrims (‘palmers’ in the contemporary parlance) are going there, rather:
    ...from every shires end
Of Engelond to Cauntebury they wende,
The holy blissful martyr for to seke
That hem hath holpen
whan that they were sick.
(From every shire’s end of England to Canterbury they go, to seek the holy blissful martyr that has helped them when they were sick.)
The martyr in question was Saint Thomas Becket, archbishop under Henry II, who, during a great power struggle between the king and the church back in the twelfth century, was slain in the grounds of the cathedral by knights who had heard the king rant ‘Who will rid me of this troublesome prelate?’, or Norman French words to that effect, and – we can’t be sure about this – either misinterpreted his meaning, or interpreted it exactly right. Soon after his death, a great cult arose around Becket, who was duly sainted, and the king had to perform a grovelling act of penance, on his knees in the mud by the Cathedral. 
The story of Becket’s death is told in T.S. Eliot’s Murder in the Cathedral, rather beautifully, although ambivalently, for Eliot was an Anglican who sympathized with the Plantagenet king’s cause, if not his methods, but Becket’s story is only ever glanced at in The Canterbury Tales, first because everybody in his time would have known it, and second because the pilgrimage was really only a kind of plot     device – in 14th Century England it was the most conceivable reason a host of different people would come together and share their stories. Indeed, if you come to The Canterbury Tales looking for religious instruction – well, you will find it in there somewhere, but you will have to sift through a wealth of profane, sometimes near-obscene, material to get there, from Arthurian Legend and Greek mythology to bawdy tales and toilet humour.  Chaucer was devout enough but interested in all of humanity, and wise enough to know that, even on the route to a holy site, religion may not be foremost on everybody’s mind.
Indeed, as another poet hinted, all sorts could happen on the way to or from a holy site:
As you came from the holy land
Of Walsinghame, 
Met you not with my true love
By the way you came?

How shall I know your true love,
That have met many
As I went to the holy land,
That have come, that have gone?

So starts the simple, pretty and bleak lyrical ballad of Sir Walter Raleigh, in which he goes on to sing of the passing of youth and the fickleness of young love. It is intriguing that Raleigh sets the poem on the pilgrimage route to England’s greatest Marian shrine, Walsingham Abbey in Norfolk, for by his era this was part of a past from which England had been decisively cut off. By the Elizabethan age in which Raleigh thrived that once commonplace activity was nigh on treasonous. Walsingham Abbey, once thronged with pilgrims there to see its replica of the Holy House, was closed for business and already falling into ruin, but its fall was less than half a century gone, and there were plenty who still rued its decline. A contemporary poem:
Bitter, bitter, O , to behold
The grass to grow
Where the walls of Walsingham
So stately did show

The above lines are from a poem lamenting the ruin Walsingham Abbey following the Dissolution of the Monasteries in the reign of Henry VIII.  England is scattered with such monuments to the age of the medieval monasteries that came so abruptly to an end, when the king and his counsellors, having broken with Rome, far more than his forebear Henry II had ever dreamed of, connived to put church property into the hands of their allies. These grand skeletal structures, sometimes blackened by soot, more often sinking into the grass, are popular sites for tourists or for pre-wedding shoots – young couples pout and simper to the camera where once the walls of Walsingham, Whitby and Fountains Abbey so stately did show.
The poet is anonymous but is thought to have been the Earl of Arundel, who converted to Catholicism in the Reign of Elizabeth I and wasted away in the Tower of London, put there on some never-proven treason charge. There are few poems in the Elizabethan era regretting the Catholicism of the recent past, perhaps precisely because expressing such sentiments could be viewed as treasonous.(An odd and slightly creepy coincidence: the man who led the investigations that led to the earl’s imprisonment went by the name of Sir Francis Walsingham.) The historian Eamon Duffy, among others, has picked up the subtlest of allusions to the dissolution of the monasteries in Shakespeare’s Sonnet 73, where he describes “Bare ruin’d choirs, where late the sweet birds sang”, which alludes to the great chantries in the abbeys, where monks once sang for the souls of the dead (William Byrd was, by the way, the foremost songwriter of his age, and a known Catholic). It may have been inspired by lines in the Walsingham poem, too:
Owls do shriek where the sweetest hymns 
Lately were sung
Toads and serpents hold their dens,
Where the palmers did throng
But Shakespeare did not write about the monasteries: their skeletal frames merely serve as the vehicle of a metaphor – he is actually describing his ageing body as he tries to woo a younger lover. 
Written two centuries after Raleigh, Shakespeare and Arundel’s, the most well-known English poem involving an abbey is William Wordsworth’s Lines composed a few miles above Tintern Abbey, but the poet, sitting enjoying the woods and hills, the memory of his last visit there, and various sublime thoughts, seems barely to notice the abbey itself, or to consider its history. He compensates for this somewhat in a later poem, The White Doe of Rylstone, which tells the story of the devastating defeat of one great northern family in the Rising of the North of 1569, a rather desperate and ill-conceived plot to return England to Catholicism by toppling Elizabeth and put the Mary Queen of Scots on the throne, and of a mysterious white doe that walks through a ruined abbey:
Here walks amid the mournful waste
Of prostrate altars, shrines defaced,
And floors encumbered with rich show
Of fret-work imagery laid low;
Paces softly, or makes halt,
By fractured cell, or tomb, or vault;

By plate of monumental brass
Dim-gleaming among weeds and grass

Though it was not among his best-known, Wordsworth considered The White Doe of Rylstone one of his best works, and indeed, it includes some lines of great beauty – as with those quoted above, which describe quite poignantly how the abbeys may have looked after their despoliation. The poem’s feeling, however, is the gentle, perhaps pleasurable, melancholy of an antiquarian: Wordsworth was no Catholic revivalist, rather he enjoyed the traces, bleak as they may be, of England’s medieval past, the same way he and his fellow romantics would enjoy the memory of Ancient Greece or Arthurian legend.
Later in the nineteenth century, Gerard Manley Hopkins wrote, though never finished, a short verse drama based on the life of Saint Winifred, a 7th century Welsh saint, a noblewoman who, the legend goes was beheaded by a prince after refusing to marry him, but who miraculously returned to life and became a great abbess.  Hopkins was inspired by visits to Saint Winifred’s Well in Wales, and of course Hopkins, being a devout Catholic, really did hope for a return of the days of saints, pilgrims and holy wells to Britain. In the drama, Winifred’s uncle Bueno, after avenging her death and witnessing her resurrection, talks of how the well he stands by will become a great pilgrimage site:
Here to this holy well shall pilgrimages be,
And not from purple Wales only, nor from elmy England,
But from beyond the seas, Erin, France and Flanders, everywhere,
Pilgrims, still pilgrims, more pilgrims still more poor pilgrims

And though this is the voice of a seventh-century Welsh prince foretelling the great popularity of his niece’s holy site, this is also the voice of Hopkins, in the19th century, hoping for a rebirth of English and Welsh Catholicism:
As sure as what is most sure, sure as that spring primroses
Shall new-dapple next year, sure as tomorrow morning, 
Amongst come-back again things, things with a revival, things with a recovery, 
Thy name

And Hopkins got his wish, or partially so, for among the day-trippers and selfie-takers at Winifred’s Well, Lindisfarne, Tintern Abbey and Canterbury a steady trickle of new pilgrims come.

The Canterbury Tales, Geoffrey Chaucer, Ed. Jill Mann, Penguin, London 2005
You may find Duffy’s analysis of Shakespeare’s sonnet in Saints, Sacrilege and Sedition, Eamon Duffy, Bloomsbury, London 2012
Walter Raleigh’s As you came from the holy land and the anonymous Walsingham lament are both from The New Oxford Book of
Sixteenth century verse, ed. Emrys Jones, OUP, Oxford, 1991
The Major works, Gerard Manley Hopkins, OUP, Oxford, 2002 (Copyright – The Society of Jesus)
Wordsworth’s long poem doesn’t make many anthologies – you can find it on the Internet!