At first the plants looked like something was eating them, maybe weevils? However, I didn't find any weevils or weevil larvae.
It is hard to say, as the pictures aren't clear enough to see the damage, but it looks like it could be a mealybug infestation. These articles will help: https://www.gardeningknowhow.com/plant-problems/pests/insects/mealybugs-control.htm
https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm
https://www.gardeningknowhow.com/special/organic/what-are-organic-pesticides.htm
Mature b.thunberii now over 3m high - is it possible to prune hard back to say 1m?
This article will tell you how to do rejuvenation pruning. It consists of removing the oldest canes first to the ground, thereby encouraging new growth. Cutting off the top will just enourage more leggy growth.
https://www.gardeningknowhow.com/ornamental/shrubs/shgen/trimming-overgrown-shrub.htm
Unimaginative suggestions! Arborvitae, forsythia...
All plants have the capacity to become invasive given the right climate. It would be very unfair to gardeners in areas that these are not invasive if we were to leave out information on the subject. Very often, new cultivars are released that are not invasive.
also, my barberry has a lot of moss and lichen - time to replace?
Their lifespan is around 15 to 20 years or so. Usually, the lichens are not harming the tree, but they are a sign that the tree is suffering from something else. This can be old age, or infection. If the shrub is around the age of 20 years, then it may be on its way out.
As long as the small tree did not die from disease, it will be safe to plant again.
This article will help you to care for these plants: https://www.gardeningknowhow.com/ornamental/shrubs/barberry/barberry-shrub-care-tips.htm
We have a Berberis which up to three weeks ago was very healthy. Now the leaves have started to drop off. We had a previous problem with sawfly. That was a couple of years ago. The only thing I have done is watered it due to the hot weather.
I'm afraid that overwatering is likely the culprit here.
They will only need water once the soil has dried significantly. The soil should be very dry, completely, down to about 5 or 6 inches or so before the shrub will need extra water.
I would recommend light pruning, and a fungicide.
These articles will help:
https://www.gardeningknowhow.com/ornamental/shrubs/barberry/barberry-shrub-care-tips.htm
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
https://www.gardeningknowhow.com/garden-how-to/info/homemade-fungicide.htm
I have been told this is a Barberry - it is usually beautiful but for some reason is being destroyed by something. The leaves are turning white and shriveling. See photos of good and bad sections. Is there anything I can do to stop the problem?
It could be the fungal disease powdery mildew that is covering the leaves in a white coating. Normally this happens if a plant gets too much shade or high humidity. Barberries prefer full sun to part shade.
If just a few stems are affected, you can prune those out. Remember, too, the plant will lose its leaves this fall anyway. Be sure to pick up and discard any infected leaves that fall to the ground. Powdery mildew does not usually kill a plant, but severe cases can damage a plant.
Here are other ways to manage:
I have two different kinds of barberry bushes that I just planted a month ago that seem to be not doing so well and I'm wondering what is wrong with them. Leaves seem burnt on the darker one and other one seems to be shriveling up from the inside (lower leaves). I have fertilized with miracle grow and water them (probably not regularly though). I have the same bushes just a few feet away that seem to be doing much better.
Unfortunately, your photo did not come through. Without seeing the damage, I have to assume fertilizer burn from your description. These shrubs do not benefit from feeding, and doing so can harm the shrub.
This article will help you with their care:
https://www.gardeningknowhow.com/ornamental/shrubs/barberry/barberry-shrub-care-tips.htm
This article will help you to, better, understand fertilizer burn:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/fertilizer-burn-in-gardens.htm