How liable would we be in the case of a fire?

Helen, I would say to contact your local Fire & Rescue Service and run it past them. As it would be them who you'd rely on in the event of a fire, you might as well ask for their advice before any such issue could arise. Their primary interest is safety, not selling you 'solutions'. If they're happy, you can be happy too - that you checked things out - and didn't rely on your own judgment (which I certainly wouldn't do!) How would you know what traps to look out for?

I write as a freeholder and fire risk assessor. Do speak to local fire officer, and yes you should get a fire risk assessment from a qualified assessor with liability insurance ( especially important post Grenfell ) , but the fire officer will tell you that .
When were the two buildings converted to flats? In many areas including mine, additional licensing includes section 257 HMOs , which is self contained flats converted before 1991 where 66% or more flats are rented ( some councils it is 50% or more ). So do check if you need an HMO license ! If you need HMO license but haven't got one and your building is not upgraded to latest fire safety standards , then the council will not go easy on you.

My block was converted pre 1991 but I had renovated to latest building regs before licensing introduced and got a licensing exemption. I have a flat in a block where I am not the freeholder and they had not completed renovations when licensing was introduced , so that has a license .

Without knowing more details and seeing the property it is difficult to comment accurately , but if there is a shared hallway/stairway I would expect a panel fire alarm system with sensors on every floor ( including cellar if you have one ) and in every flat and separate interlinked smoke sensors in each flat. I would also want emergency lights , escape signs , arson protection ( external letter boxes ) , testing and servicing schedule for alarm and emergency lights , eicr certificate for communal electrics, fire proof electric cupboard (if you have one in communal areas )to 30mins , etc etc etc .....

If you follow advise of fire officer ( which might be more than advise , it might be compulsory ) and carry out all the actions in the fire risk assessment , then you can sleep easy that you have followed expert advise . If sadly an incident did occur , you can then prove to investigating authorities and insurance assessor that you followed expert advise.

Your buildings insurance would normally include property owners liability cover which will provide some cover.
It really depends on what exactly you are trying to cover. No insurance policy can provide cover for criminal fines but you can insure for the legal fees in defending any prosecutions by for example HSE.
Yoiu should speak to your insurance broker for further advice.

If this is a converted property then as Andrew landlord suggests, it may be covered by the s257 HMO requirements, including the Regulatory Reform (Fire Safety) Order 2005. This requires a Fire Risk Assessment to be carried out on the common parts, (entrance lobby etc). Whilst any competent person can perform this assessment, it is likely that in the event of a fire, the assessment would come under scrutiny and unless it was done by an independent professional, it may be found inadequate. Your insurance may then be affected and your liability would be in question regarding any injuries, deaths or damage to the leasehold properties.

You can do a fire risk assessment yourself but it is probably not a good idea. Speak to your Fire & Rescue Service as others above have recommended.
If anything goes wrong, it's the FRS that people (council, police etc) refer to. Try to get something in writing because of what happened to me.
Several years ago the lessees bought the freehold of a block of flats, where I owned one flat.
The FRS inspected at my request for no charge. They initially said the flat doors were already fire doors and did not need replacement. Six months later they decided that they did!