Seems like a sort of tent caterpillar. They eat the leaves under protection of the tent. I usually get the broom to them on my small apple trees as soon as I notice the tents. I don't think a hawthorn hedge is going to mind a temporary set back due to munching pests.

Hi Benidorm and welcome to GoY inside that 'cobweb' there are hundreds or even thousands of little tent caterpillars happily eating your hawthorn's leaves. If possible remove them by hand - otherwise you will need to use a spray, preferably one that only targets the caterpillar.

Oops posted together Dorjac... and you are right the hedge will survive the attack.

The tent is to protect the caterpillars from predatory birds. If you get a long pole and use it to scrape off the tent then the birds might come in and eat the caterpillars for you.