Myself and Mrs fm were discussing this just the other day - we were both told, as we were growing up, that Summer started in May
From Wikipedia:
The unofficial start of summer is a matter of convention: in Ireland it is as early as May 1, in many countries it is considered to be June 1, while in others it is as late as July 1.
Further interesting info from Wikipedia:
The Irish calendar does not observe the typical astronomical seasons (beginning, in the Northern Hemisphere, on the equinoxes and solstices), or the meteorological seasons (beginning on March 1, June 1, September 1 and December 1), but rather centres the seasons around the solstices and equinoxes (so that, for instance, midsummer falls on the summer solstice), beginning the seasons at the approximate halfway points between solstice and equinox, following the seasons of the ancient Celts (see below) which are pre-Christian in origin.
So that's why we think summer starts in May - the Irish calender starts it then