This is a typical wording for tenants liability from a leading Insurers. Most Contents Policies will include this somewhere in the policy. Under some it will be under Liability section and on others under contents.
We will pay all amounts you become legally liable to pay, as a tenant
of your home, for damage caused to the buildings during the period of
insurance shown in the schedule, by any cause covered by paragraphs
A, B1, B2 and B3 of section 1 of this policy.
For any claim resulting from one incident, we will not pay more than
20% of the total sum insured by this section
The perils covered are the standard risks under Buildings (A), Plumbing installation (B1), Locks & outside door (B2) and fees/clearance costs(B3). There are exclusions were property is let e.g theft or attempted theft by tenant.
My understanding of the cover is that if the Building is damaged and you have any legal liability conveyed to you in your tenancy agreement, this section will cover your liability. An example could be. You have left a chip pan on the gas and this causes smoke damage to the decorations. If your tenancy agreement makes you responsible, then a claim could be made against the policy. Obviously the landlord should have Buildings Insurance and normally a claim would be made against that in the first instance. I suppose then the landlords Insurance would then claim a contribution from the tenants Contents Insurance where this is relevant. I have not dealt with a claim in this circumstance, this is my understanding of how this would work.
This is the Morethan cover under Contents section
17. Tenants liability
Your liability at law under covers 1-12 of the
Buildings section of this policy, if you are
legally liable under the terms of your tenancy
agreement (not as owner, leaseholder or
landlord), for damage to your home.
I suspose the consequence of not having cover is that you could be personally liable to pay for damage to the Building under your tenancy agreement. If the landlords Insurers looked at the tenancy agreement and noted your liability, they could pursue you for a contribution if you were negligent. Therefore it would be sensible to take out Contents Insurance as I think it stipulates in your tenancy agreement.
One last point here. We are not talking about accidental damage here. If you damage the Building or landlords Contents, accidently, you could lose any deposit. Landords fitting & fixtures are not covered by your Contents insurance, the landlord has to arrange their own Insurance.
Hope this helps