Although Blackie is initially very angry about the way that he has been deposed from his position as the leader of the gang by the upstart T., and is aware of "the fickleness of favour," he quickly gets over his anger and rejoins the gang in their task. If we look at the text carefully, we can see his reasons for doing this:
...but suppose after all what T. proposed was possible--nothing like it had ever been done before. The fame of the Wormsley Common car-park gang would surely reach around London. There would be headlines in the papers. Even the grown-up gangs who ran the bettering at the all-in wrestling and the barrow-boys would hear with respect of how Old Misery's house had been destroyed. Driven by the pure, simple, and altruistic ambition of fame for the gang, Blackie came back to where T. stood in the shadow of Misery's wall.
Thus it is that Blackie is inspired by the potential success of T.'s plan and the respect and fame it would win for the gang if it is successful. To him, this is worth more than his own feelings of anger at losing his position of leadership. Because T.'s plan is something that has never been done before and that it is on such a monumental scale, it would ensure the fame of his gang. To be part of that would definitely be worth the humility he needs to summon up to rejoin the gang and work under T.'s leadership.
Just for your knowledge the correct way is "The Destructors?" *
Blackie didn't return home after losing his position because:
1. If the gang achieved their goal under T.'s leadership the whole gang will be appreciated.
2. Everyone involved in the gang will get the credit for achieving their goal.
3. It was time they found a new leader. To test his ability of leading he wanted to stay as a part of the gang.