Some church-goers at St Patrick's in Soho Square have received dispensations from the parish priest, excusing them from the rule that meat should not be consumed on Lenten Fridays.
Fr Alexander Sherbrooke from the church said he had not been publicly promoting dispensations, however, he had granted them to those who had asked him for one.
Speaking on Premier's News Hour, he added: "I think it has to be a parish which is dedicated to St Patrick [who has permission to grant dispensations]; the parish priest can give dispensation in that place.
"Or, indeed, the bishop of the diocese can give dispensation but it depends very much on the local bishop."
Corned beef and cabbage is traditionally eat by some Irish families on St Patrick's Day, however, every seven years the saint's day coincides with a Friday in Lent.
The issue has been dubbed the "corned beef conundrum" in the United States, a country which boasts a significant Irish diaspora.
In the US, Catholic leaders have publicly disagreed over the issue of dispensations regarding the eating of meat on St Patrick's Day.
While the Archdioceses of Denver in Colorafe and Lincoln in Nebraska have said they are not granting dispensations for St Patrick's Day, others have agreed to, according to the Catholic News Agency.
Catholics in the Archdioceses of Omaha in Nebraska and Washington DC, however, are being asked to hold their day of abstinence on 18th March, if they choose to eat meat on St Patrick's Day.
Fr Alexander from St Patrick's went on to say: "Most people will simply be in the practise of abstaining from meat on a Friday.
"[They] would celebrate joyfully but wouldn't worry too much about indulging today but I'm sure they would have a glass of Guiness to celebrate."
St Patrick's Day celebrations have been taking place across the world including at a parade on the streets of Dublin.
Elsewhere, the Duke and Duchess of Cambridge took part in St Patrick's Day celebrations after meeting soldiers of the 1st Battalion Irish Guards.
Click here to listen to Premier's Alex Williams speaking with Fr Alexander Sherbrooke: