I have always understood the camping at the school to be reserved for booked morris sides and booked performers only. The nearest touring caravan site I know is the other side of Rochester airport, near Bluebell Hill, way way way too far to walk in, on a quiet-ish back road with no bus service.

There is a nice big flat level block of land right by the Medway that has been grassed and has access roads and some water standpipes, and it is doing nothing because it is earmarked for development of which thanks to the banking system there is none at the moment. It was there last year too. Alas one is not allowed to use it for tents or caravans although it needs only a security guard on each entrance to keep urban yoof off.

There is quite a bit of space that would do for tents just outside castle gardens, and it has been used for markets and so on in the past - but you are not allowed to camp on it.

The King's School has nearby playing fields - but you are not allowed to use them.

There is a recreation ground down Short's Way - but you are not allowed to camp on it.

The Great lines in Gillingham are in bussing distance - but you are not allowed to use them.

In summary, I suspect that council policy is that they only want people who can afford to hotel or B&B as they have presumably more money to spend.