It has been estimated that at least 1,000 people in Britain and Ireland are the children of Roman Catholic priests according to the Guardian Newspaper.

The issue of celibacy in the church will come up during the pope’s visit to Britain says the Guardian who quotes the children of priests saying that it must be addressed.

There are three common Irish names,", "McEntaggart, McAnespie and McNab, that translate as 'son of the priest', 'son of the Bishop' and 'son of the Abbot', so it's been around for some time." says former Catholic priest Father Pat Buckley of Northern Ireland who left the church in part because of celibacy issues.

It already has in Italy. In May of this year dozens of Italian women banded together and sent an open letter to the Vatican calling for the abolition of celibacy.
This Italian women had been in relationships with priests of lay monks and argued that a man “needs to live with his fellow human beings, experience feelings, love and be loved,” according to the Guardian.
Their letter also pleaded for sympathy for those who “live out in secrecy those few moments the priest manages to grant [us], and experience on a daily basis the doubts, fears and insecurities of our men.”
The topic of celibacy has also been a topic of constant debate as clerical abuse scandals have swept across even corner of the Catholic Church and critics link sexual frustration to pedophilia.
There are also those who defend celibacy in the early Christian Church. Pope Benedict has said that celibacy “is made possible by the grace of God . . . who asks us to transcend ourselves." He believes that abstaining from marriage shows a commitment to the Church.
For those women who have been involved with men in the Church and children who are denied by their father’s there is a lack of financial support and recognition. There are very few support groups to help their cause and they make little headway with the Church.
In Larne, Northern Ireland there is what Pat Buckley, an excommunicated gay priest and the organizer calls an “independent ministry to disaffected and alienated Catholics and Christians". He has been running this group since the 1980s and also runs a support group for women who are in relationships with priests.
He said "These problems have been hidden for centuries, but there's been so much in the news that people are getting a bit more courage to come forward."
For example, in Ireland, in 1992, there was the case of Eamon Casey, the much loved Bishop of Galway, who had used diocese funds to pay maintenance for his American child.
Buckley believes the Catholic Church plans to "hang on to celibacy for reasons of power and control. St Paul said in one of his letters that a bishop should be the husband of one woman. If a man does not have the experience of running a human family how can he run a church? Celibacy was unusual during the first 12 centuries of the Catholic Church. It was introduced [in the Middle Ages]. It's often very sad for the women and children in these relationships. A lot of them want some form of resolution, to sort out the baggage. Anybody who is abandoned by a parent suffers a
very large injustice.”
Of course there is the other side of these argument, those who defend celibacy in the Church. Father Stephen Wang is the Dean of Studies at Allen Hall seminary in London. On his blog earlier this year he wrote “there are practical aspects to celibacy. You've got more time for other people, and more time for prayer. You can get up at three in the morning to visit someone in hospital without worrying about how this will affect your marriage . . . But celibacy is something much deeper as well. There is a place in your heart, in your very being, that you have given to Christ and to the people you meet as a priest."