The first thing you should do is check your eligibility to travel visa free under the Visa Waiver Program – http://london.usembassy.gov/cons_new/visa/visa_wizard.html. If you still require a visa, you should call the Operator Assisted Information Service for assistance stating the nature of the emergency.
A limited number of appointments are available daily for those who have genuine humanitarian need of travel. The number to call is 09042-450100 from within the United Kingdom (Calls cost £1.20/min from BT landlines; some mobile and network providers may charge more). For those in the United States, please call 1-866-382-3589. Callers are charged a fixed rate of $16:00. Payment is by credit card – Visa, MasterCard, American Express only.