Broadly speaking, it's to spread the "tax burden" around so no one group feels unduly "picked on" in meeting a country's tax requirements.
Without getting into a debate on the rights and wrongs of taxation (and in particularly what level of services a country/state should provide, and what should be self-funded by the individual), the generally accepted position is that a country/government needs a certain amount of tax revenue each year to "make the country work". Taxes can come from a variety of sources (e.g. capital gains tax, corporation tax, income tax, sales tax/VAT etc.) but at the end of the day, a given amount of money needs to be raised.
Considering just corporation tax (tax on the profits of businesses) and income tax (tax on individuals' earnings), there are essentially three ways a government could raise £20,000 towards its tax requirements: tax the company only, tax the individual only, or tax both.
Grossly simplifying things, assuming the company makes £100,000 profit before wages, and an employee earns £40,000 "take home" per year...
Corporation Tax @ 33% / Income Tax 0%
After paying un-taxed wages of £40,000, the company has a taxable profit of £60,000, of which one-third goes in taxes (£20,000) and the company is left with £40,000.
Coporation Tax @ 0% / Income Tax @ 33%
The company pays pre-tax wages of £60,000, of which one third is paid by the employee in taxes (£20,000) and they get to keep £40,000. The company is left with £40,000 which isn't taxed.
Corporation Tax @ 20% / Income Tax @ 20%
The company pays pre-tax wages of £50,000, of which one fifth is paid by the employee in taxes (£10,000) and they get to keep £40,000. The company is left with £50,000 of which one fifth goes in taxes (£10,000) and £40,000 it can keep.
In all cases, the company is left with £40,000, the employee is left with £40,000 and the total taxes raised is £20,000. However, in the first case the company probably feels victimised (because only it pays taxes) and in the second case the employee feels victimised (because only he or she pays taxes). In the last case, while neither the employer nor the employee is probably "happy", at least they are both sharing the burden.