One US mile per gallon is 1.2009 imperial miles per gallon. Both units count miles travelled per gallon burned, and the entire difference is that the imperial gallon is twenty per cent larger than the American one.
About the units
The US gallon is exactly 3.785411784 litres, descended from the English wine gallon of 231 cubic inches standardised in 1707. The imperial gallon is exactly 4.54609 litres, created by the British Weights and Measures Act of 1824 and originally defined as the volume of ten pounds of water. The United States had been independent for nearly fifty years by then and kept the older definition, so the two never reconciled. Every unit built on the gallon inherits the split, and fuel economy is where it is most visible to consumers.
The exact factor
The ratio is exactly 4.54609 ÷ 3.785411784 = 1.2009499255, the same figure that separates the gallons themselves. A car rated at 30 US mpg is 36 imperial mpg. Rated at 40 US mpg it is 48 imperial. Unlike the conversions to litres per 100 km, this one IS a simple multiplication, because both units are efficiency units built the same way — only the gallon differs. That makes it the one straightforward conversion in the whole fuel category.
Where you meet this conversion
Comparing American and British road tests of the same vehicle, which is the main case and a genuine source of confusion in motoring journalism. A car that reviews at 45 mpg in Britain and 37 mpg in America has not changed; only the gallon has. Manufacturer specifications for globally sold models list both. Historic fuel economy data needs care, since American figures carry a different gallon and a test method that has been revised in several steps — the ratings began in the mid-1970s and the procedure was reworked in 1985 and again in 2008, the latter cutting quoted city figures by ten to twenty per cent without any car changing.