I've set up a run coaching business so have quite a bit of experience here. To coach children you'll need a coach qualification - the leader/coaching assistant qualifications only insure you to work under the supervision of a coach. You'd need to check which one permits coaching of under 12s - I think it is the athletics coach one. You have to get a DBS as part of the qualification process and you have to do safeguarding course (you'd also need a safeguarding policy). Once you have all this you'd be covered by EA public liability insurance.
What you may find an issue is that you'd really need to have someone working with you for safeguarding/health and safety reasons, and therefore if you want to make this a viable business you'd have to think about whether it would be financially viable. Lots of running/athletics clubs have junior sections that are free/minimal charge, and that is the market you'd be operating in. I had orginally intended my business to focus on coaching children but I just couldn't see a way of making it viable. Schools are often looking for people to provide after school clubs for them but in this day of limited budgets and the rise of 'PE apprentices' who they pay £99 a week, many pay peanuts. I was offered £7 to run a one hour club in one school, which wouldn't even have covered my petrol costs. I gave up on the idea of coaching children and focused on the adult side of my business instead.
Do you have a coaching qualification? If you want to run a kids' club you can't just do the one day leader in running fitness because I think you are only insured to lead over 12s. But if you do the two day coaching assistant I think you will be insured. They will also go through other requirements like DBS check which you can do through England Athletics, and also as you said first aid course. Another option might be to run it out of a school and you may be able to piggy back off their insurance?
I have no experience with self employment. No idea what I need to do. My son is a keen runner but there are no groups locally so I thought I'd look into starting one.
A quick search tells me I will need public liability insurance, dbs check. A good idea to have some policies. First aid training. How would one go about sorting out taxes etc. I really have zero experience or knowledge of anything like this so any help at all would be great. Thank you