Ohhh, sounds fun! Do you mean essentials as in besides the normal tent, sleeping bag, clothes, first aid kit, flashlights, batteries, sunscreen, etc..? Are you seriously roughing it or just camping at a campground that has bathrooms, showers, tent areas? Here's some things I can think of that you may not come up with if you haven't done this before, I'm sure others will have plenty to add!
Bandanas/scarves to tie over your hair. Both to keep bugs out (don't know if you have tick problems in the UK like we do in the US), the sun off your hair/scalp, and as a fashionable way to disguise the less-than-fresh hair when you aren't close to a bathhouse!
A tarp to put under the ground, beneath your tent. Most newbie campers don't think of this and then find their tent bottoms messed up by rocks and such.
Cayenne pepper to sprinkle around the outer base of your tent, or some sort of bug spray. Helps keep ants from making a home of your tent! Also, bug spray for your body!
If your tent doesn't already include it, patches in case you get a hole are very valuable! And a sealer to spray on the fabric to make sure the seams are water tight.
Biodegradable soap (like Dr. Bronner's castile soap). Lets you wash things up and toss the water without killing the grass or polluting the surrounding water supply. Unscented baby wipes, they have a zillion uses! Biodegradable ones are even better. Toilet paper-I know you'd think campground bathrooms would have plenty, but depending on where you're at, some places I've noticed slack off and don't stock well. Hand sanitizer.
Rope and laundry bag to string your food up in a tree. Or a sealable tote to store your food in, in the car! Don't take any food in your tent, or you might have unexpected company!

A wash basin & sponge is a good thing to pack too, and a "mess kit", i.e. eating utensils and plastic/metal dishes.
Things to leave at home: Heavily scented items like lotion, perfume, body spray, even perfumed deodorants. Best to buy unscented bath and body products to take camping with you. We all love to smell good, but some scents attract bees and other bugs, plus can be overwhelming in the heat of summer camping.