The most common British usage is:

pud·ding, n.
1.
a.A sweet dessert, usually containing flour or a cereal product, that has been boiled, steamed, or baked.
b.A mixture with a soft, puddinglike consistency.

I get the impression that British food is not highly regarded in the States, but the British make the world's best puddings.

Other recommended highpoints for British cooking are breakfast (it was, I think, Napoleon who said the way to eat well in Britain is eat three breakfasts a day), and the curry. London curry-houses are said to be the best in the world, and that includes India.