Hello NP, welcome to the forum!
OK dokey, it looks like you've got a few things going on here. First off, I have a couple of questions: how much have you been watering and feeding these plants?
Cherry laurel thrives on poor, pretty dry soil and can experience problems if life gets too easy for it, like a dog that gets fed on pizza and mars bars. New plants do need regular watering while they establish their roots, but not so that the soil is soggy the whole time. Let the top two inches or so of the soil dry out before watering again, or to put it another way, water thoroughly and infrequently, not a little every day.
It's a similar story with feeding them: if your soil is decent and you improved it a bit before planting, they don't need any extra food.
I suspect that these plants have been over pampered, would that be right?
I think that they've been hit by a double whammy of shot hole and mildew. Since your plants are young and you want them to get off to a good start, I would suggest using a fungicide to give them a hand (mature plants can be clipped to help control these issues, but that's not much of an option for you).
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No great cause for concern here, your plants will be fine.