Yes, the closest car parks are as follows:

• Intelli Park, Parker Mews, WC2B 5NT (Recommended):
  1 minute walk. If you arrive before 9:30am, you pay £15 to park all day.
• Urban Parking, Shelton Street, WC2H 9HJ:
  2 minute walk. All day entry is £54.
• APCOA, Museum Street, WC1A 1RJ:
  4 minute walk. All day entry is £28.
• Q-Park, Bedfordbury, WC2N 4HX:
  9 minute walk. All day entry is £44.