Paying once covers the car for the day, as many trips as you like. And I'm not sure the average of £4.00 is right; I don't know what proportion is eligible for discounts.

Anyway, there was never any doubt about why it was introduced. The post was created by the government largely to sort out London's transport, but was given no budget to do it. They had to raise revenue somehow, and the government get the job done (I hope!) without it appearing to be them who have imposed the extra tax. As one who lives in London, I don't see those who imposed the congestion charge as "robbing gits", I see the government as having pulled a very clever blame-transference scam.