Here is a link to information about a special license. The following extract can be found at the bottom of the page.

"To marry outside the normal hours, or in a private chapel, ... required a special licence, granted at the discretion of the Archbishop of Canterbury. A special licence would mean a trip to the Faculty Office in London, making a sworn statement (the marriage allegation), and paying a very hefty fee, but if an immediate or private marriage was the only course open to a couple, they really had little choice."

Darcy's connection and wealth makes marriage by special license possible.