"However, it's not too late for David Cameron to turn this around and leave an environmental legacy he can be proud of," she said.No, no, no.
"He can start by reigning in his chancellor, who seems hell-bent on trashing the environment."
'Reign' is what the Queen does. It means 'rule' and is related to the Latin rex or regina, king and queen. It's almost an anagram of regina. Perhaps that will help. "Reign in" makes no sense.
'Rein' is what you have on a horse to control the bridle. To stop or slow the animal, you pull on the reins, or "rein in" the horse.
From the context, I am sure Black intended that Cameron should slow down or stop his chancellor (shouldn't that have a capital 'C'?), rather than have him rule the country from his living room.
(HMTQ: As it is tipping it down outside, we propose to reign in for the afternoon.)
A hundred lines, Black, "I will learn to spell proper, like" and homework is to find out that 'homophone' means. No, not that, stupid boy ...