Hi, My name is ***** ***** I am happy to assist you.
If you are unsure of how to locate your TSA Precheck number since you fly with Delta I have provided the link so you can easily let the other airlines know when booking your flights that number.
I assume you will be booking online so make sure to add that to the Known Traveler Number field.
It still will not guarantee that you will get pre check status but you will atleast have it in the profile for any travel coming up.
https://universalenroll.dhs.gov/programs/precheck Then hit locate KTN
There are a few airlines do not participate in the TSA Precheck and British is one of them.
So British would not be one that you would need to contact. Here is the list of participating airlines :
TSA Pre✓® participating airlines include Aeromexico, Air Canada, Alaska Airlines, Allegiant Airlines, American Airlines, Cape Air, Delta Air Lines, Etihad Airways, Hawaiian Airlines, JetBlue Airways, Seaborne Airlines, Southwest Airlines, Sun Country Airlines, United Airlines, Virgin America and WestJet.