Why is income tax so high? (UK)
In the UK, government spending is 38.5 per cent of GDP.  To oversimplify, that means that for every £1 spent on private goods, 63p needs to be raised in taxes.  At present, the UK raises a little over a quarter of that from income tax.  One of the reasons income tax is a significant component is that it is progressive, unlike other major sources such as VAT and excise duties.

It is also worth mentioning that the categories of government expenditure you mention are relatively small.  Half of all government spending goes on pensions, healthcare and education.  The categories you mention are marginal by comparison.