This happens after a 3 day trip from Ireland which can lead us to assume he didn't arrive to England but most certainly mainland Europe. Is there any place or particular reason that made possible for them not to encounter any one for that amount of time?
The Confession [Latin] is a weird autobiographical text, generally assumed to have been written by Patrick himself (along with his so-called Letter to Coroticus—everything else about him was written much later). It seems to have been written as a defense against some sort of charges charges or slander, though it's not entirely clear what Patrick was defending himself against. Despite the title "Confession," he doesn't admit to any particularly glaring acts of wrongdoing. Perhaps it's considered a confession because he attributes many of the events of his life to the intervention of God, in which case it might be seen as a humble admission of his own lack of responsibility; maybe Patrick's detractors had accused him of being proud and ungodly.
At any rate, the passage in question comes from chapter 19. Patrick has already narrated his youth, growing up in a family of deacons and priests (likely in Wales or the West Country), being captured and sold into slavery in Ireland, tending sheep for six years, leaving (escaping seems too strong a word for a shepherd abandoning his flock), and securing passage out of Ireland. He would later become a bishop, go back to Ireland, and worked to establish the Christian faith there.
That brings us to chapter 19 itself. After three days—a triduum—Patrick says, he and his shipmates reached land. From a literal standpoint, this would likely keep them in the Irish Sea, somewhere between Glasgow in the north and Plymouth in the West Country if they sailed from Dublin. But keeping in mind that Dublin didn't yet exist and that they might just as well have been rowing, this probably puts them much closer in the vicinity of Wales. At any rate, the narrative suggests that Patrick was close to home and had no further noteworthy legs to his journey after this one, so I think it places us somewhere on the island of Britain.
The term triduum is, of course, also used to describe the three days preceding Easter, when Christ has been laid in the tomb but is not yet resurrected, and the number three has many other significant resonances as well, so it's not necessary to assume that this description is meant to be taken literally. Twenty eight, in contrast, doesn't appear prominently in the Bible, but it is the number of days in a lunar cycle. The church-educated, Latin-literate readers of Patrick's Confession would have known that immediately, since the lunar calendar was definitively important for annual calculations of the proper date to celebrate Easter—which might have reinforced the suggested link between Patrick's time at sea and Christ's time in the tomb. These are two suffering servants.
Patrick continues to describe his 28-day sojourn as taking him through a desert—here meaning a place without people, not a place without water—and his group ran out of food. He then says, "famine overcame them," apparently quoting a passage from his version of the Book of Genesis describing the journeys of Abram (Gen 12,10).
This description, therefore, has clear resonances with biblical and liturgical life. If they seem obscure to you and me, it's worth remembering that Patrick was writing in Latin, so all his readers would have been elite, educated churchmen. And since there weren't many copies of the bible circulating yet in Britain, it's safe to assume that they knew and discussed the particular passages Patrick decided to quote, including this one. We don't have very many other texts from this time, so there's little to tell us precisely what this passage signified to Patrick or his audience, but it certainly had some nuanced sort of significance.
Patrick and other early churchmen were sensitive to these kinds of biblical allusions, but they also saw the bible as containing literal truths, and Patrick's description of western Britain as a desert likewise held a grain of truth as well. We know from later British texts from the 600s and 700s that "desert" could refer to places that were actually lightly inhabited and sometimes heavily trafficked, such as the hermitages of Cuthbert near Lindisfarne and Guthlac in the Fens. So we're probably not talking about an absolute wilderness.
In context, this is a wilderness because Patrick and his shipmates are unable to find a steady source of food. In Roman Britain, a group of hungry travelers would have two options: find a city where food could be purchased or find a villa where a Romano-British aristocrat could support the group. Both kinds of sites were rapidly abandoned in the mid-400s, which is the likely timeframe of Patrick's life. Farmers, finding sudden relief from Roman demands for surplus agricultural produce, turned their attentions instead to household crafts like pottery production to make up for the collapse of Roman supply chains that had previously provided all sorts of everyday goods. This seems to have been the widespread shift in both Britain and Gaul (France) north of the Loire River. Patrick and his shipmates might have found farms to shelter them and maybe even feed them for short periods, but they would have been hard placed to find people capable of providing any sort of enduring support.
So what then is going on in this passage? Well, the specific language helps paint Patrick in the same light as Christ and an Old Testament patriarch, possibly even pointing to Patrick's role in one of the recurring debates about the correct calculation of the Easter date. There also seems to be an acknowledgement that Roman social systems have collapsed, and perhaps a hope that bishops in Britain and Ireland would rise to fill this power vacuum, much as they did in parts of southern Gaul, Italy, and Iberia.