When I lived in FH and shopped at Sainsburys (and Savacentre) I was always very worried about their storage conditions. I frequently had cartons of milk go off within a short time despite the dates on it. in one case by the next day before it had even been opened.
Since moving to Norwich and shopping in Tesco a 4 pint carton of milk easily lasts until its use by date, often a week from purchase. In 6 years I've not had a single carton go off.
Sainsburys FH stock rotation often leaves a lot to be desired. I once found a whole shelf of bottled salad dressings that was 6 months past its Best Before date.