As a data point, going two ways between zones 3 and 1 by tube is 8.7 pounds a day, and it will go up soon. If you include 2 people in the family, the convenience of dropping off the kids at their schools, etc 15 pounds doesn't sound that bad for the car, if you have where to park.
It is not any more expensive than anywhere else in central London. Electric cars can drive in the city for free at any time. For other cars, between 7am and 6pm you have to pay a £15 congestion charge to drive in the centre. You might have to pay another £12.50 ULEZ charge if you drive an older car.
You should be made to pay extra healthcare taxes for driving an ICE car in an inner city area since you are the primary contributor to a lot of extra cancer cases.