Limited metered parking is available on some of the surrounding streets. The closest car parks are:
Lincoln's Inn, Lincoln's Inn Fields WC2A 3TL (020 7693 5108)
NCP, Covent Garden http://www.ncp.co.uk/find-a-car-park/car-parks/london-covent-garden/
The Peacock Theatre is inside the congestion charge zone, and a fee is payable between 7am - 6.00pm Monday to Friday, excluding Public Holidays. For details: https://tfl.gov.uk/modes/driving/congestion-charge/congestion-charge-zone
For up to date travel information or to plan your journey, visit TFL Journey Planner.