Liability Insurance, etc, on Flats where Council owns the Freehold

Other

Hope someone can help with this query. I own a couple of ex-council maisonettes, where it is mandatory that I pay the council/housing assoc. to insure the property against major damage. But it does not provide cover - I believe - public or employer's liability, nor for minor issues. My broker says that insurers will only provide comprehensive cover - i.e including the cover which I already have with the council - and I don't want to pay twice!! Can anyone advise if/how I should proceed, pls?
Thx!!