It is possible, although UKBA do not encourage it (see text below), to apply and pay for priority processing after you have submitted your application:
"We do not encourage you to purchase the priority service after you have submitted your application. Where necessary, you can elect to purchase the priority service after submitting your application. If you purchase the priority service after submitting your application you must:
fax a copy of your receipt to 212-754-3062; and
include the relevant tracking number(s) for the package containing your application and supporting documents."
Here's where I found this information:
http://www.ukba.homeoffice.gov.uk/countries/usa/worldbridge-services/?langname=UK%20EnglishI believe I have read here of applicants who went down this route, perhaps a search would turn up someone who was successful?
Good luck!