Powdery Mildew is (unsurprisingly) a grey, powdery fungal coating that affects a wide range of plants including native hedge plants, such as hawthorn, field maple and wild roses as well as ornamentals such as beech
and laurel. There is probably no hedging plant that is immune. Mildew is not a serious condition and is usually easily dealt with either by spraying with a suitable fungicide (there will be at least 4 or 5 brands on sale in your local garden centre) or by doing nothing and waiting for it to go away. Which it will when the underlying causes have been dealt with or removed.
Paradoxically mildew, which is a fungus, often attacks as a result of plants having been dry underfoot. They become stressed and weakened and so are easy targets. So mildew in hot dry weather is best treated with a good watering. In the longer term (and a number of these pages say the same thing), incorporate more well rotted organic matter in to your soil. The more the merrier. It will increase the water holding capacity of the ground and so reduces the stress your plants suffer in dry spells. With native hedge plants, the easiest way to do this is to chuck your grass clippings along the bottom of the hedge. Give your ornamentals and soft fruit a mulch of well rotted compost or manure
The other reason you find mildew is because air movement around the diseased plant is poor. This is why it more often attacks climbing roses, sheltered against a wall, than bush roses which are out in the open. Spraying works, as does judicious pruning to remove overgrown parts of climbing plants. By the same token, mildew often affects thick, well trimmed native hedging. This is a backhanded compliment to the hedge - dense hedges allow less air movement.