this looks to be a good guide to fire safety in HMOs including compartmentalisation rules
http://www.safelincs.co.uk/fire-safety-information-for-landlords/
looks like it really boils down to whether the building is interpreted as being a low risk household, larger property etc. which would be pretty subjective.
A long history of operation without any fire incidents ought to help to demonstrate that it should be classified as a relatively low risk property.
at a minimum I'd think you should have interlinked smoke and heat detecting fire alarm throughout the main risk areas of the building, and stair way, emergency lighting in the stairway, fire extinguishuers and blankets in stairwell etc. As long as the ceilings, walls etc are solidly plastered, and the doors to the main corridors are solid that should probably be ok for a low risk building.
If you've got an external fire escape out the back, then there should be no need for compartmentalisation IMO, asssuming each floor has fire exists onto the escape route, as you don't need a 30 minute fire rated corridor for people to escape through - they can get straight out to the fire escape.
that's my quick thoughts, not that I'm personally an expert, but have had to deal with fire safety law for using buildings for public events, so learnt about 30 minute fire corridors etc for that.
As I've said,I do have an expert on hand in the form of my dad, who's taught a good proportion of the fire safety officers and consultants in the country.