Although council tax is paid by tenants (as it's a tax on residents rather than owners) it impacts rents. The burden of council tax is thereby shared by both tenants and landlords.

Two similar apartments on opposite sides of the same street can have significantly different market rents just because they are in different boroughs, and those boroughs have vastly different council taxes. The classic example in London used to be Wandsworth vs. Lambeth.

Council tax, although based on properties, is meant to be a tax on residents, to put towards local services like police and rubbish collection. It was created after a previous tax (dubbed the 'poll tax'), which taxed each individual, regardless of the size of their abode, caused protests.

Window tax[0] also does not work. Driving around the country you will see houses with broken out or boarded up windows so the owners didn't have to pay the tax. The tax was repealed in 1851 but the damage from it can still be seen.

[0] http://en.wikipedia.org/wiki/Window_tax

Nar, he means a land-value tax, which is raised from time to time in the UK.