Theresa May's pledge comes ahead of a summit where EU leaders will assess the progress made so far.
There was an average of 100,000 crimes a week in the year to June, the Office for National Statistics says.
The singer tells the BBC an encounter early in his career made him feel "terrible".
Two-thirds of all fly-tipping involved household waste that was commonly dumped at the side of roads.
The move would make the country the first part of the UK to outlaw the physical punishment of children.