I am worried since I have spotted this web on my neighbours, fairly young box shrubs. If this is the dreaded box caterpillar then I need to act fast as I have some serious topiary of a good age a little way from their bushes.
Look for the frass (poo) which is like tiny little green balls and which you will see on the ground below the plant. The caterpillars have to be picked off by hand but in my experience are not easy to find. If caught early enough your plants will be fine, but perhaps look a bit scrappy for a while. Would be more afraid of Blight.