 Bermingham was the son of Francis Bermingham, 14th Baron Athenry, by his first marriage to Lady Mary Nugent, daughter of Thomas Nugent, 4th Earl of Westmeath.He was elected to the Irish House of Commons as Member of Parliament for Galway County, sitting between 1745 and 1750, when on 4 March 1750 he succeeded his father as Baron Athenry and became a member of the Irish House of Lords.He was invested as a member of the Privy Council of Ireland, but was ejected from it in 1767 by Lord Townshend, the newly arrived Lord Lieutenant of Ireland, who wished to make a "clean sweep" of the Irish administration, removing all those he regarded as corrupt or inefficient.