MummyPig, I have the good fortune to have children that far prefer the rest of the gardens to Climbers and Creepers. The area around Queen Charlotte's cottage is rather nice, as is the Japanese garden with the big gates. There's a human-size badger sett to crawl round, and in the summer there's a treetop walk. And do try out the bamboo musical instruments around the traditional Japanese house (nowhere near the garden with the big gates). And there are lots of food plants (bananas, babacos, oranges etc) in the palm house. And I'm sure every self-respecting child just has to love the primordial soup in the evolution house.
If you want to get away from C&C, you could try allowing your children to choose the direction every time there's a choice of paths, then see where you end up. Or take the road train. Or even "Follow That Peacock" (though I have noticed they quite often end up in the gift shop - specially trained to encourage visitors to spend money I expect...)