insurance by Ocaso through my freeholder (local authority) - is it enough?

I let out an ex-council leasehold flat. As I understand is usual with leasehold, it is insured through the freeholder (which in this case is the London Borough of Tower Hamlets). The insurer is Ocaso and the insurance is subject to the general conditions of their Household Building Insurance for Local Authorities. I am noted as the insured party. The policy is very similar to that here: http://www.ealing.gov.uk/downloads/d...itions_booklet

As far as I can tell, the wording of the policy does allow for the insured party to be a landlord as opposed to be an owner-occupier, which is a good start! I am aware that it doesn't cover contents, non-payment of rent, legal expenses, emergency repairs etc. but for various reasons I don't require any of those to be insured. What I am worried about, however, is do I have sufficient property owner's liability insurance under this, in terms of potential liability to my tenants? Page 11 of the linked document covers these issues but I just can't work out whether it would cover any liability I might have to my tenants (as opposed to visitors/neighbours/tradesmen/passers by).

I appreciate this is quite a boring technical question but I would be super grateful if an insurance expert could help me out on this.