Each state has their own hunters education program, usually this includes some classroom work (or online course work) as well as some time in the field with an actual weapon. These courses are mostly frequented by young new hunters (like 10 to 14 years old) with a handful of older people.
I have taken courses in California, Oregon and Arizona. A large part of the course is usually related to firearm and or archery safety. Another part usually has to do with some familiarization with wildlife conservation.
I took the Arizona course a few years ago since Arizona give you better odds of drawing a tag (an extra "bonus point" for the draw) if you have taken their Hunters Safety course. The neat thing about Arizona is I was able to take the course work online, then fly down for a single day of testing in the field (handling a weapon, some shooting, identifying safe and unsafe shooting situations, and a written test).
The courses I have been to usually have a near 100% passing rate.
I am not aware of a Hunters Safety course that can be done completely remotely (I see you are in the UK), but some of the other guys may be able to help you in this area.
When applying for a hunt in various states, you need to see what their hunters safety education rules are. Each state has it's own rules. In some states it is only required up to a certain age. Some states have more strict rules.