Plenty of shrubs flower in May/June - but its hard to be sure quite when a lot of years because of the weather. For instance, a Weigela in a client's garden is looking stunning right now, in full flower and has been for a week - last year it didn't flower till the end of May and looked great in early June. That said, a few to consider would be Weigela varieties, Escallonia varieties, Choisya ternata, Hebe youngii