get on like a house on fire
have a harmonious relationship (UK; sich sehr gut verstehen)
"Thanks for introducing me to Frieda. We get on like a house on fire."
This idiom is a play on words, using two British expressions.
To get on (well) with someone is to have a harmonious relationship with that person. You feel comfortable around each other.
• Jen and I get on really well. We always laugh about the same things.
• How are you two getting on?
To get on (with something) is to make progress.
• How are you getting on with the project?
• How are you getting on?
A house can burn down quickly as fire spreads from one part of it to another. So if two people get on like a house on fire, they have met recently and are discovering more and more things that they like about each other.
The equivalent expressions in America use the word "along" instead of "on".
• I wish we got along better.
• How is the project coming along?
If two Americans get along very well, we say they get along swimmingly.