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To be pedantic, there aren't actually any regs for the dimensions of a bike plate. All that's specified as far as size goes is that it must be 2 lines ('letterbox' is definitely illegal), size and font of the characters (smaller than car spec), minimum space between them and minimum margin around them. All that of course effectively defines the size of a plate but if you have a 6-character registration like mine you can legally have a narrower one as it's only 3 characters across instead of 4.
Precisely the arguments I went through some years ago with the police and DVLA, not over a bike plate but over a plate on an American car.
U.S. car plates have been standardized at 12 x 6 inches since 1957, so frames and recesses are designed to take that size plate. Larger plates simply do not fit properly in many cases, especially when recessed into a bumper, doubling as the cover for a centrally mounted filler cap, etc.
The number I had was a 7-digit "Q" number, all with fairly wide characters such as 3, G, E, etc. The only way you could possibly meet the height and spacing specifications would be to use a shorter number or one with a lot more narrow characters, such as 1.
Fortunately, this is one instance where lobbying from American car clubs actually paid off, and the regulations were amended a few years ago to permit slightly smaller characters on imported vehicles with restricted plate sizes.