I work as a ltd company and can tell you that I pay corporation tax and income tax under self assessment, so you are potentially wrong on that as well and on top of that, HMRC also get VAT from my labour. Not very good way of tax avoidance is it?
Corporation tax is lower than income tax, though, and - as a company director - you can get a significant tax free right-off. Plus you can alter your tax affairs so that you avoid higher rate taxation to a lesser or greater degree and claim substantial tax free deductions often on things you'd just have paid for as an employee. If you're not paying less tax as a contractor through a ltd company than you would as a direct employee you're doing something wrong.
The striking thing about it all is how voluntary tax is as a contractor. By tweaking your returns one way or another you can make huge differences in how much tax you pay. Which results in the bizarre situation of preparing one return for the mortgage application and another for the taxman.
Some difference in taxation levels seems fair enough since, as a contractor, you forgo the right to benefits for six months after you stop working and some other differences but the system can function as a method of mere tax avoidance.