Well there's military.. but outside of that? Scouts? That system has been severly questioned and is being or has been over hauled due to deaths..
Outside of that... the MLTB's are the main providers.. in mountain biking its less centralised..
No you don't have to 'prove' anything..
You have to 'prove' currentness of first aid knowledge. Not mountain knowledge. You are assumed to have stayed current. There is no reason why a guide who passed his ML in 1965, and is a current first aider can't work as an ML..
Anyway you do not need qualifications at all.. if people want to guide based on experience that's perfectly OK in the UK. Your insurance will need to know and will be more expensive and probably more specific, but the main worry is stating accredited courses as being relevant to leading runs out in the hills..