Eg Say you pay yourself £4,000 Salary - no tax (or NI) as below your personal allowance and the rest in dividends then you dont pay income tax - the company would already have paid the corporation tax on the dividend.
Look at things from a different perspective: You own stock in Big Corporation. Big Corporation pays you a dividend of 1000 Pounds. Aren't you required to pay tax on that income?
I'm in the States, so I don't know all the aspects of the U.K. tax system, but I know in the U.S. it's the same thing- corporate dividends are taxable.