I don't think it is necessarily a problem of sweetened drinlks. The US has increased their overall sugar intake and much of that rise is from beverages (many containing high fructose syrup) but this doesn't apply in either Australia or the UK, but they have similar problems to the US.
In both countres the consumption of added sugars has fallen (( from 1980-2003 by 16% in Australia and 5 in the UK.)In Australia , children's consumption of sugar laden drinks has halved over the last decade.
What has risen in Australia (and I suspect in the UK) is the proportion of calories from chocolate, cakes and cookies, pizza and packet chips(crisps). These are all high density foods.. lots of calories from a mixture of fat and carbohydrates.
A tax on industrial junk foods might be better but this would really hurt some with low incomes who, wisely or not, rely on these products. Ideally it would be better if the tax gained were used to subsidise fresh produce. ( but how?)
Education must be important, but most people actually know that these things shouldn't form the basis of their diet. Can there be anyone who hasn't heard of Jamie Oliver and his crusade against processed foods?