I suggest this is because the towbar companies listings are out of date - the One was a 1.4 many years ago. I believe the One and the Cooper count as the same car for towbar purposes and what fits one fits the other.
You can confirm the maximum towing capacity that Mini allow by looking at the VIN plate in the left door shut. This lists four weights in kg in the following order:
- Gross Vehicle Weight (the maximum loaded weight of the car)
- Gross Train Weight (the maximum loaded weight of car and trailer combined)
- Front Axle Weight (the maximum loaded weight of the two front wheels), often with '1-' in front
- Rear Axle Weight (you can guess this one, can't you?), often with '2-' in front
Deduct Gross Vehicle Weight from Gross Train Weight and you have the maximum trailer weight. Mini may allow a higher trailer weight than this (ie, that can be towed by a car when it is not loaded to its own maximum) - look in the handbook for that.
There are some models that Mini has not bothered to approve for towing, such as S hatchbacks or all Convertibles/Coupés/Roadsters, so they have a blank line for Gross Train Weight (see photo) since that does not apply to a car not approved for towing.
However please note that the trailer that Mini says it is OK to tow and the trailer that your driving licence allows you to tow are two completely different things. The licence restrictions are now so complicated that you need to individually look up what you can tow, based on when you passed your driving test at https://www.gov.uk/towing-with-car
If you just want to tow a small baggage trailer, which is likely to be much less than 750kg loaded, then none of this is a worry as you will be well below any trailer weight limits.