"Burnbake campsite is full," said a woman's voice on the answering machine. "We do not take bookings. We will change the message when pitches become available."

Last weekend marked a couple of significant firsts for my family. We decided to make our first trip to the Isle of Purbeck, the Dorset peninsula to the south of Poole Harbour, a fossil's-throw from the Jurassic Coast. And, for the first time in nine years as a parent, I left my front door with only the vaguest idea of where we'd be spending the night.

We'd been planning a camping trip to mark the end of the half-term week. The weather forecast looked good and we'd set our hearts on Burnbake as a result of a decent write-up in the Cool Camping England guide. It seemed a good location from which to explore the beach resort of Swanage and the sands of Studland Bay, and – more importantly – it promised a selection of secluded woody glades in which we could pitch our tent. But that lady on the answering machine was a bit of a concern. I phoned round some less woody-gladed alternatives, and soon got the message: Dorset was packed to the max, tent-wise – and, no, it didn't take bookings.

Never mind, I thought, as we packed a jumbo-sized tent and two boys into the back of the Volvo. We'd go anyway. After all, the sun was shining and at the very least we'd have a day of sandcastle-building before sleeping under a hedgerow en famille.

Upon reaching Dorset, I ignored the host of "site full" signs leading up to Burnbake, and parked the car rather firmly next to a couple who were packing up their tent. Then we waited, ready to pounce. So what if their pitch was next to the children's playground and the toilet block? The place was heaving with campers, and our quiet woody glade would have to be sacrificed at the altar of expediency.

However, within minutes of building our canvas home and filling it with sleeping bags, it became clear that there were in fact plenty of people leaving. Indeed, woody glades were becoming available all over the place. So, slightly humiliatingly – and much to the bemusement of our children – we unpegged the tent and carried it, semi-erect, 100 yards to the right before re-pitching it in the very woody glade we'd been promised in the brochure.

Accommodation sorted, we spent two days exploring Purbeck itself. Despite the campsite exodus, last Saturday's high temperatures brought plenty of visitors to Studland Bay's Knoll Beach, which swiftly became a jarring clutter of windbreaks and inflatable boats. But brooding Corfe Castle was impressive – and the view of the ruins over lunch at the Scott Arms in nearby Kingston was worth any amount of campsite angst. The high point was a walk from the village of Acton to Seacombe, a stunning amphitheatre quarried from the limestone cliffs, and on to Dancing Ledge, where the children splashed around the rough-hewn swimming pool. We even strayed beyond Purbeck to the croissant-shaped Lulworth Cove, where we found a tiny fossil.

And our woody glade? There's probably room for a few more campers there now, if you fancy it.

Next weekend: pitches at Burnbake (01929 480570; burnbake.com), Rempstone, Corfe Castle, Dorset BH20 5JH cost from £10 per night.