If birch is pruned now, it will ooze a sap which can weaken the plant.
When it comes to pruning Buddleja davidii some gardeners, especially new gardeners, are very nervous about pruning it hard, but this is exactly what the plant requires. Flowers form on the ends of new growth made in the current year.
If you left a butterfly bush unpruned the flowers will appear higher, and you’ll not be able to enjoy them properly. You want the flowers at a manageable height, so look around the base of the plant for new buds or shoots. Prune back to these.
First, reduce the height of the existing shrub by removing half of the growth. Then, using clean, sharp secateurs and a pruning saw cut stems back to just above a bud, close to the ground.