I think you are missing the point and holding the laffer curve wrong here.
The justification for the congestion charge in London was to reduce congestion, not raise revenue. The laffer curve says that as you increase the rate, the activity of the thing you are taxing decreases and so revenue decreases with it. So therefore if they increase the fee, congestion should decrease if you believe the laffer curve applies here. If they wanted to reduce congestion, just set the fee to the far right of the laffer curve and watch as congestion decreases (even if they raise no money as a result)
But actually they have not reduced congestion at all in the long term. Instead they've optimised the fee for the peak or the "sweet spot" (t* in your linked article) where they can get the most money out of it, not decrease congestion the most. They've raised the fee to the point where there has been no change in behaviour/congestion, and they make the most amount of money they can. If they raise the fee more they start to reduce their revenue as congestion drops due to shifting to the right of the curve.
They could very easily increase the fee and drive down congestion based on the laffer curve if that is what they really wanted, yet they don't. From this we can make the fairly strong assumption that this is not about reducing congestion , it's about extracting the optimum amount of money. Meanwhile congestion is basically the same as it was before the congestion charge was introduced, except now TfL get £15 per car per day as a nice bonus to fund the various vanity projects.