You need to follow the local laws regarding marriage license application. Go to the Town Registrar for details. It varies, but generally it requires a party to reside in a place where the license is issued for the marriage for 30 days. There are other circumstances that allow variations.
The quickest means for getting married-with a proper license in the UK, is to elope to Gretna Green. There the marriage could proceed almost immediately.
The only other places where a marriage could be agreed quicker are Las Vegas, NV and Elko, NV. These marriages would still be legally recognized by the British government.