I am a resident of Bergen County in NJ that seems to be the source of many of the cars driving into Manhattan. Many parts of Bergen County (on the northeastern side especially) are not well served by buses into the city. But I think that even if bus service were iproved, it might not have much impact. Most of the people driving to the city are extremely wealthy people as is easily visible by the amazing number of luxury cars you see along the roads here.
Then we'll be happy to collect a little of that wealth for the priviledge of driving into Midtown.
In London, parking costs you £25 per day (but many people get it thrown in by their company)

conversely the congestion charge is £8.

(multiply by 2 to get USD equivalents).

The Congestion Charge has reduced traffic by 10-15%, but more in the off peak than the on peak.

The conclusion?  Those who can afford to drive to work, still drive to work.  Parking was already their biggest bill.

In economic terms, they are highly price inelastic consumers.  The additional cost is offset by the fact that they can get to work faster (lower traffic).

The discouragement has been on voluntary trips, trips by servicemen and builders, trips 'passing through' the centre, shopping trips etc.

I've been thinking about it, and congestion charging is seeming to me like not all that great an idea, and definitely not the solution to Manhattan's traffic problem. Well, it all depends on how you define "Manhattan's traffic problem". If you define it as "cars are moving too slowly" then yes, it might help a bit, because the benefit from removing that last 10-15% of cars is relatively high. But if you define the problem as "there are way too many cars in Manhattan", then it's not a very good solution at all: you'll have only a bit fewer cars, but they'll be moving faster. It seems like other,  and possibly better, solutions involve taking street space away from cars, and giving it over to wider sidewalks, bike lanes, and dedicated (and separated) bus and streetcar lanes. Of course, there's no single solution to this problem, and the singleminded focus on congestion charging really isn't helpful.
Bingo!

You've hit a nail on the head, I suspect.

Jane Jacobs wrote about this before she died (see 'The Coming Dark Age').  Jane Jacobs, along with Betty Friedan, Rachel Carson, Diane Arbus, Germain Greer and a few others was one of those women who changed the world, a group of women who grew up in the old world, became housewives, mothers, and got dragged willy nilly into changing the world.

New York (and Toronto) owe her a great debt.

Basically roads are traffic generative.  Close a road and  some of the traffic disappears.

We will shilly shally around with 'free market' solutions, which make great sense in terms of the economics I was taught.

And we will then find, that to increase the number of journeys, to get an acceptable throughput of people (and not incidentally to confront global warming) we are going to have to do something really, really radical.

Like ride bicycles.

One thing that nobody seems to have suggested for congestion charging is somehow scaling the charge by income. A trivial way to do this is by charging differently for different types of cars, but there are more direct ways to link the charge with income as well. The advantage of this move is that it at one stroke completely gets rid of the opposition's "what about the poor people who can barely afford a car" argument. And scaling charges to income is not completely without precedent: fines for traffic violations in Finland work like that, and some Nokia executive got a million-dollar speeding ticket once.
How about giving low income folks free passes for the transit system and cutting all fares for everyone else?  Have the congestion charge make up for the lost revenue.
London again.

Revenues from the Congestion Charge haven't met expectations.  Traffic fell by more than expected (but not at peak hours).  Costs of running the system have been higher than forecast.

Meanwhile the system is flooded with low cost users (kids under 16 are free on buses, also those over 65 etc.).  But the transit system (at peak) is 100% capacity.  Kiley (former head of the NY Transit, imported to run ours) told the Mayor this would happen, but our Mayor is an ex Trotskyist demagogue (think of him as a Rudi Giuliani of the Left).

Another nuance is we now have double length 'bendy buses' to replace the conductor on the old Routemaster double decker.  As a result (you get on and off at any door) I would estimate at least 1/3rd of riders are not paying (you don't pay a fine often enough to make it worth paying).  Maybe over half of riders on some routes.

Difficult to administer and too easy to cheat, I suspect.

Scandinavian societies are high homogeneity, with high compliance to laws.  New York is a high heterogenity, low compliance to laws kind of place (OK it's not Lagos, but compared to most major western European cities).

Systems and social programmes that work in Scandinavia and in Singapore, don't work so well in freewheeling 'Merica.