Hi busybeingmum - I have just got back from a lovely little campsite in Crawley, Winchester, which is a 45 min drive from Beaulieu.
Folly Farm Touring Caravan Park Crawley Winchester Hampshire SO21 2PH
Tel: 01962 776486
It has a kitchen that is open 24 hours a day for microwave, toaster & kettle. Toilets and showers. Electric Hookup if needed.
Very spacious, no defined pitches unless you want hookup. Climbing frame, etc.
We booked last Thursday afternoon to arrive Friday. No time restrictions for arriving or leaving (as long as after 06.30 am). Gate is kept locked at night to protect children, and closed in day.
There is a field with cows/ horses and chickens roam free.
It cost us £16 per night for a massive 8 man tent. The staff are lovely, and Leon showed us around the site when we arrived. They ask you where you would like to camp with regards to the children's needs.
I'd highly recommend it as long as you are not looking for a massively high-tech experience.