I think what would determine child poverty is that oh so new labour but such good term, "social exclusion".
I agree with everyone else's absolute poverty definitions, but I also think that poverty is relative. So if a child is socially excluded (not being able to go on school trips, have holidays, family outings, occasional treats) because of lack of money, then that too is poverty, albeit not so dire as the absolute type.
I think the government are doing some very tiny things to address it by ever so slightly raising benefit levels for families, and the introduction of tax credits, which I think has been the single biggest factor in making some poor families less poor.
I'd argue that we do still have lack of clothing/ shoes and food, and cold.
Lots of families cannot afford heating and have to turn the heating off and put up with a cold house - JK Rowling famously wrote her first Harry Potter book in the local library because she couldn't afford to heat her house. Many very poor families never buy new clothes (except underwear), buying all clothes second hand from charity shops or relying on donations from friends and family.
Lack of food might not be an issue, but lack of good food most certainly is. Lots of very poor areas are "food deserts" where it is impossible to get fresh fruit and vegetables, so people live off poor quality processed, canned and frozen food, much of which is high fat, high energy and low nutrient.
HTH - sounds like an interesting essay!