If you go back to work/change jobs then you should not have to tell the government departments. With use of IT nowadays when an employer gets a p45/p60 it should register on a database where Tax rebates and Tax credits will be paid from. When the person leaves the company just remove the NINO from the database. All the HR department should have do is register the NINO to the system and the HMRC pays out what the person is entitled to. All the employee would have to do would be register their child.
Why is this idea important?
It is important because some people forget to do so as soon as they go back to work.
Makes the employers life easier as well as the HR dept. That way ALL companies would have to register not only companies who earn more than 15k a year. If they make less than that then they would be sole traders.