In US English, a common say to say it is "this food has spoiled" or "this food is spoiled." As is so often the case, the description as "British" is misleading. "To go off" isn't frequent, but it's understood. However, "off" is quite common. I might very well say to my wife "Does this milk smell a little bit off to you?" In US usage, "off" means that the food smells bad. Also, we are apt to use specific descriptions of specific ways things are spoiled. Milk is "sour." Fruit is "rotten." Eggs are "rotten." Bread is "moldy" (US spelling, British would be "mouldy") if it has colored patches of mold on it. Bread or cake is "stale" if it has gotten dried out and hard. Crackers are "soggy" if they have gotten damp and are no longer crisp and crunchy. For meat or chicken I would probably say "has gone bad." Theoretically the right word is "putrid." However, "spoiled" is a good general word.

Many people also use the expression, "this has gone bad!' For example, a husband might tell his wife, "I think this milk has GONE BAD" The expression sounds grammatically incorrect but, nevertheless, it is a common expression!

I would use "to spoil." E.g. The meat will spoil if you don't keep it in the fridge.