"Lilliburlero had a very strong political impact"
Some of the information I gathered for a talk on Song and History" on the song which is said to have "sung a king out of three nations".
Jim Carroll

According to legend this tune first appears in 1641 in Ulster. Richard Talbot (1630-1691), a Catholic and royalist, had been made Earl of Tyrconnel after the Restoration and King James II later appointed him Lord Lieutenant of Ireland (1686). He pursued strong pro-Catholic policies. Even after James was deposed in England Tyrconnel governed Ireland in James' name. Irish Catholic forces were eventually defeated by William. English and Irish Protestants took up the song as their melody during that time.
According to one source the words "lillibulero" and "bullen al-a" were used as a rallying cry for the Irish to recognize one another in the uprising in 1641. Later (1687) Thomas, Lord Wharton (1640-1715), wrote a set of satirical verses titled Lillibolero regarding the Irish problems and set them to a melody arranged by Henry Purcell in 1678. Purcell's arrangement was based on an older tune under the name Quickstep which appeared in Robert Carr's Delightful Companion (1686). It became popular immediately. After the Stuarts were deposed, Lord Wharton, a strong supporter of William III, boasted that he had "rhymed James out of three kingdoms" with his tune.*
However, Irish writer Brendan Behan claimed the words of the chorus were a corruption of the Gaelic: "An lili ba leir e, ba linn an la" - roughly "The lily won the day for us."** A forum post at Digital Tradition reveals that according to Sources of Irish Traditional Music (1998) it translates as: Lilli/ bu le'ir o/, bu linn an la/ - Lilli will be manifest, the day will be ours. William Lilly (1602-1681) was a famous astrologer who made predictions regarding British politics of the time. One prediction was the Prophecy of the White King (made in 1644 after Marston Moor), which predicted a King would be beheaded or killed. Lilly wrote a letter to Charles I warning him of the prophecy Anther theory, from Songs That Made History by H. E. Piggot, states the refrain came from a popular Irish song when James II (a Roman Catholic) came to the throne which had the Irish words, "Lere, lere, burlere." Lere meant religion or faith and burlere meant your faith. Piggot says a form of the tune was printed in 1661 in An Antidote against Melancholy which was set to words beginning There was an old man of Waltham Cross.
Wharton never publicly supported the Stuarts. As a member of the House of Commons Wharton supported the bill to bar James from the succession because of his Catholicism. When William won the war, Wharton was given prominent posts. There is speculation that Wharton referred to the Lilly prophecy, and used the Gaelic words to disguise them because when he wrote the words the Stuarts were still in power.
John Gay used the tune in The Beggar's Opera. It was the British Broadcasting Corporation's signature theme during World War II.
"Brother Teague" was then the nickname of the Irishmen (as "John Bull" would later be for Englishmen).