It's the driver's responsibility to pay for the congestion charge, which is not included in the rental price.
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.
Drivers must pay £11.50 in advance, or on the day of travel, or £14 by midnight on the following charging day, on www.tfl.gov.uk
If this isn't paid, you will receive a Penalty Charge Notice (PCN). To find out more about handling PCNs, go to this article.