Unfortunately a company called Air Sunshine have taken YI. If that combination of letters had still been available then I would have started a company called Geordie Airlines which would operate a single flight from Newcastle just so I could call it YI001.
You might have to be British to get that one.
If not, you can at least benefit from this list of USA-UK flights ordered by destinations and details of which airlines serve them. Next time I'm flying between Manchester and JFK, I'm going with Pakistan International.