"British" and "Base" Horsepower do not exist. BHP has always been Brake Horse Power due to the method of measurement of peak developed power (read on).

The horse power is an imperial (i.e., British) unit of measurement anyway, derived from a mythical horse's ability to pull a hundredweight of coal a known vertical distance up an incline in a measured time. This allowed a calculation of the rate of work, and the peak power developed by the horse doing the pulling. (The alternate way to measure power is to brake the rotating object to (almost) stalling point. Given the measured radius of the rotator, and the force applied, the torque could be calculated, and then the power developed.)

I joke not, in the early 1800's during the Industrial revolution, this was the way people could assess the capability of one of the 20 million (no spelling mistake or shifted decimal point) equine inhabitants of the British Isles at this time. Prior to the introduction of the static or mobile steam engine, the horse was the staple motive power, with the population of horse almost equalling that of human on that small island (side note: this is how the Brits have established such a strong relationship with the horse, and will no doubt explain countless jokes about the British, their gardening habits, Roses and the best way to grow them, Shakespere's references to horse flesh, and many other curiosities of that small island). The assay of a horse's worth inevitably depended on a health assessment of teeth and hoof by a vet, followed by a pulling power test at the local assay yard. These inclined planes still exist around the country. Various large engineering structures around the UK take the form of inclined planes set at a standard angle to allow horses to perform under measured conditions, and allow (for example), mine owners to assess the maximum possible load a given pair or four would be able to tow up or down an incline to a canal or railway basin.

After steam became the prime motive power (then later IC engines) the unit of power measurement stuck. The population of horses dwindled extremely rapidly to a fraction of their previous count, but their legacy is recorded in buildings and structures all over the country in coaching houses, large stables and livery yards, horse markets and donkey mills. Even up to the middle of the Stalingrad offensive, they were still used as the prime mover of choice for armies and artillery pieces (on all sides; the Polish army retained a mounted cavalry which was used to charge German tanks and machine guns during the invasion of Poland). One of the primary reasons for the inability of the beseiging German 6th Army's to break out of the Russian Kessel offensive (an encirclement) was that 120,000 horses used to tow artillery pieces into the battle zone at the start of the campaign were moved out of the forward area to reduce the logistics overhead of providing fodder and stabling materials, and to free army stable hands to fight the German offensive on the city. It was done by the Wehrmacht bureacracy as a cost cutting measure!