This question has been answered by a student from Edinburgh University.
Thank you for your question! I am a student here at the University and a convert to Catholicism. My background was middle-of-the-road Anglican but I often attended Walsingham. Some of the most beautiful spiritual experiences of my life have occurred there in the shrine that the Anglicans have.
It is beautiful and it is, in almost every sense ‘Catholic.’ This is unsurprising since when the strand within Anglicanism known as ‘Anglo-Catholicism’ developed they looked to what the Catholic Church was doing in terms of liturgy and devotion. One could easily mistakenly wander into the Anglican shrine at Walsingham and mistake it for a Catholic Church.
The difference, is as you say, that they don’t mind not having a ‘pope.’ But that difference is far more important than they themselves realise: it comes down to authority. Many within the Anglican communion regard what happens at Walsingham idolatrous. There used to be protests there during the procession of the statue of Our Lady of Walsingham.
As Catholics, however, we can be confident that our practices are the same practices which (with some development, obviously) go right back to the earliest times of the Church. We have the same Faith, again with developments, that streteches far back into the Church’s history. We have our bishop who can trace his lineage back to the Apostles and a Pope who is the symbol of our unity in Christ.
The position of the Pope within the Church might at first seem trivial but it is far more important than many would realise.