Overflowing bath in upstairs flat, no contents insurance

Hi

A friend of mine rents a ground floor flat, and has had an incident with a considerable amount of water coming through the ceiling from the flat above.  The upstairs flat was out when the problem occurred, and my friend called a non-emergency police number, and they came round and broke into that flat. 

The police told my friend that the bath had been left running and overflowed.  The woman who owns and occupies the upstairs flat later said that she had turned the bath on and put the plug in when the water had been turned off earlier in the day, when the water company was doing some work in the area, and had then gone out without turning it off.

Most of the damage was to carpets and paintwork, and the landlord is dealing with that.  However my friend has no contents insurance, and has had some damage to bedding and furniture - the furniture at least is not completely ruined as I understand it, but there is a fair amount of staining.  She is documenting everything she can with photographs.

With no contents insurance, but with a problem that was clearly caused by the owner of the upstairs flat, what if any recourse does she have?  She has been given the insurance details for the upstairs flat's contents insurance policy and has been told by that company to write to them setting out the damage and the reasons why it was the fault of the upstairs flat.

Is the upstairs flat's insurance likely to pay out in this situation, or should the upstairs flat's occupier be approached directly?  And is an overflowing bath something for which one or both are liable for?

Also, is it reasonable to ask for replacement of partially damaged furniture?  If not, what other remedy would be appropriate?

Extremely grateful for any answers...