The London Palladium is within the London Congestion Charge Zone which applies from 7am until 6pm and costs £11.50 per day. If you are driving to the theatre after 6pm then you will not be charged.
The London Palladium is part of the Q-Park Scheme. The nearest participating car park is the 24hr Q Park Chinatown Car Park (20 Newport Place,WC2H 7PR). Parking costs £18 for up to 3hrs, and £24 for 4hrs but theatregoers can save 50% if they have their tickets validated at the theatre.