Tier 4 Priority Visa PILOT program timeline

Hello-

Intro: I am an incoming American student at Cambridge. Early last week, I submitted my visa application online and had my biometric appointment last thursday (August 30). That same day, I sent my application via courier to the UK's New York embassy in order to officially submit my application. On Tuesday of this week (September 4), I received a notification from UPS stating that my application had arrived at the office in NY. However, only today did I receive any sort of confirmation from the "UK Visas and Immigration" office in New York saying that my application is, "is being assembled and prepared for assessment." This delay is somewhat shocking, as I sent the application more than a week ago via UPS 1 day air.

Some important details: I purchased the "priority" processing package, and my sponsoring institution, University of Cambridge, is one of 4 schools that maintain membership in the "tier 4 expedited processing program," which required fewer documents for the application.

The problem: I am scheduled to fly to the UK on September 16. Today is September 7. That leaves only 9 days, and 5 business days, for me to receive my visa. When I sent my application in via courier last week, I figured that more than 2.5 weeks would be enough time considering the fact that I had purchased priority processing AND was being evaluated under the pilot program. I am now starting to worry.

Generally, how long do priority t4 applications to to be processed?