You are correct. The assurance scheme they all go with is BRC Global Standard for food safety. Unless it is a small producer in which case they tend to go for SALSA. SALSA is of course part owned by BRC!I'd be very surprised if you could supply any major supermarket without some assurance scheme, they will demand it just to cover their own backs at the very least. They will have their own set of rules you must follow if they choose not to use RT.
If you have various customers that all require assurance of some sort it can be beneficial to be RT assured as you then only have one scheme to follow, what usually happens is each customer sends their own questionnaire with extra questions each year. We decided to stop supplying Booths because the time spent answering the bloody questions they asked made it not worth bothering with them.