One imperial cup is exactly 284.130625 millilitres. It is the largest of the cups in common reference, twenty per cent bigger than the American one, and it is the reason old British and Canadian recipes go wrong when read with a modern measuring set.
About the units
The imperial cup is half an imperial pint, or 10 imperial fluid ounces. The imperial pint is 568.261 ml, which comes from the imperial gallon of 4.54609 litres — originally defined as the volume occupied by ten pounds of water at a specified temperature. That water-based definition is what separates the whole imperial liquid system from the American one, which descends from the English wine gallon of 231 cubic inches instead. The imperial cup is effectively obsolete in British recipe writing today, where weights in grams have taken over, but it persists in older cookbooks and in Canadian recipes from before metrication.
The exact factor
The exact value is 284.130625 ml, derived as 4.54609 litres ÷ 16. Against the US cup at 236.588 ml the ratio is 1.2010, so an imperial cup is a little over one and a fifth US cups. Against the metric cup at 250 ml it is 1.1365. Those are not rounding differences: a recipe calling for three imperial cups of stock converted as US cups delivers 710 ml instead of 852 ml, a shortfall of nearly a cup and a half.
Where you meet this conversion
Older British cookbooks, particularly from before the 1970s, and Canadian recipes from the same era. Commonwealth countries that metricated later — India, parts of the Caribbean, South Africa before it adopted the metric cup — carry it in their traditional recipe literature. The practical difficulty is that these recipes rarely say "imperial": they simply say cup, and the only clue is the date and origin of the book. If a British recipe predates metrication and the quantities seem too small when made with American cups, this is usually why.