get on like a house on fire—(also: get along like a house on fire) become good friends in a very short time:
- “How are your new neighbors?” “Pretty well, their sons and ours get on like a house on fire.”
go like a house on fire—
1. (of an event, activity, etc.) be very successful:
- All the families were gathered around and the ceremony and reception went like a house on fire.
2. is used to refer to some fast action:
- Time was precious, so … I would go like a house on fire trying to say as much as I could before my time was up.