Should under 18 year olds get a minimum wage of £10 an hour?

It was announced today that if Labour get into power, they will introduce a £10 minimum wage, including for those under 18 years old.  See, for example, this guardian article.

Paul Johnson, the director of the Institute for Fiscal Studies, has attacked the £10 an hour minimum wage proposal for under 18 year olds. He asks whether people this young need £10 an hour since they'll be living with their parents.

Apart from the fact that obviously people older than 18 live with their parents too, we can argue that about anyone. Does anyone need their hourly wage if they have any savings, or if others can help them etc? Do CEO's need £10 an hour (least of all the wages they actually get) since they can clearly survive with the wealth they already have? 

It's preposterous to decide someone's wage by considering whether others will support them. And I see no moral reason why one's age should disqualify one from the safety net of a minimum wage. You have to pay wages according to the skills they have and the work they do. Age ought not to matter.