No, the Congestion Charge is not included. It is your responsibility as the driver to pay it.
The Congestion Charge is a daily fee of £11.50 between the hours of 7am and 6pm, Monday to Friday. There is no charge on public holidays, or between Christmas Day and New Year's Day. It applies to central London only and does not include the Dartford Crossing Dart Charge.
You can pay in advance, on the day of travel, or by midnight on the following charging day. If you pay in advance or by midnight on the day you travel, the Congestion Charge is £11.50. If you pay after midnight on the day you travel and before midnight on the following day, the cost will be £14.
To pay online, go to: www.tfl.gov.uk
If you don't pay by midnight on the day after you travel, the owner will receive a Penalty Charge Notice (PCN). Go to this article to see the next steps.