June is the month to watch out for the Large Skipper butterfly on Sweet William, Virginian Stock or Candytuft.
The Alliums and Chives with Hesperis matronalis were flowering at the end of May 2004 in my back garden and have attracted butterflies in June in past years. My Thyme plants in the front garden were also a mass of flowers.
Sweet Williams were just coming into flower at the start of June.
A number of shrubs, both large and small, are worth watching: Lavender, Hebe, Escallonia, Cotoneaster, Ceanothus and Buddleia alternifolia. All of them have had butterflies feeding on their flowers in June.
My Verbena bonariensis will start to flower this month.
It should also be safe to buy and plant out summer bedding like French Marigolds.