Quarter-days in England and Ireland:
(1) New Style: Lady Day (March 25th), Midsummer Day (June 24th), Michaelmas Day (September 29th), and Christmas Day (December 25th).
(2) Old Style: Old Lady Day (April 6th), Old Midsummer Day (July 6th), Old Michaelmas Day (October 11th), and Old Christmas Day (January 6th).
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Quarter-days in England and Ireland from Infoplease: