It's like loads of things I see on this site, a phrase I use all the time without thinking about it but when it comes up in a thread I haven't a clue where it comes from or why I use it. I'd love to know too.
At a guess I would say it originated from a time when narrow streets and thatched roofs were prevelant, and the spread of fire from house to house would indeed be "very fast or vigorously".
Well fanx but that's a definition not an etymology. Probably easier to find in a book than the internet, and I'm sure you lot/guys/ppl have loads of dusty old tomes full of useful info. Where's jheem? He seems to know everything.
http://users.tinyonline.co.uk/gswithenbank/sayingsl.htm "Like a house on fire - very well Originally, very quickly or vigorously; the simile made better sense in the old days when houses were of wooden construction and had thatched roofs, etc."
The phrase means 'get on well', right? But the origin suggested there does not so much imply a friendly relationship as a kind of contagion. To 'spread like houses on fire' would be more appropriate.
I recognise, however, that word origins do not have to be logical.