But...the children are friends so why wouldn't it just be considered one having the other over to play?
According to the article, this is why (and also why they say it's illegal):
This was because little-known rules say friends cannot gain a 'reward' by looking after a child for more than two hours outside the child's home without agreeing to a number of checks including one from the Criminal Records Bureau.
Although the mothers never paid each other, their job-sharing deal was judged to be a 'reward'. Campaigners fear thousands of working families could be innocently breaking the rules by relying on close friends for informal childcare.
Yes, it's still ridiculous...