Some employers consider that a significant burden. There is an argument that without it, for every seven employees in the company the employer could afford one more (whether that would be the likely outcome is an interesting debate). Alternatively it might mean they could lower prices by the equivalent margin (which in a consumer market with VAT on top would be 16.5% total) or that they could make bigger profits on which they should then be paying c. 22% corporation tax. As a general rule imposing taxes on employers for giving people work is not a good way to grow your economy.
If as Scotroutes alludes to your friends question is actually about how much tax HE pays and the employer collects on his behalf, then assuming he is earning £300/wk and earns for all 52 weeks in the tax year then:
Gross = £300
Income tax – £19
Employees NI – £17
Take home = £263
So his employer takes £36 from him, adds on their own 13.8% (£41.40) and pays the government a total of £77.40.
Still think 13.8% is low – when its more than the employee is paying in earnings based tax themselves?