There is no legal requirement for any non-government organisation to have a child protection policy. In those organisations where children are present then it is definitely within the realm of 'best practice' to have one. Sadly, most places develop one more because it covers their own back should any incident happen in the future, or any accusations be made, than because there is evidence that having such a policy enables the said organisation to do more to protect children.
Something which protects children efficiently in an 'adult club' such as a caving club is common sense.. children under 16 are only taken underground either directly under their parents' care, or by people who have specifically been authorised and requested by the parents (for example, Scout leaders where obviously child protection principles are adhered to, and consent forms taken).
The riskiest example is in the case of a family friend, who takes the child caving at the express wishes and permission of the parent. In this case, were an incident to happen or an accusation be made, unless there were anything in writing, then it would be hard to prove the parent had given permission. Also, if the family friend were a member of a cave club, then it could reflect badly on that club that their members were taking children underground without written consent/police check forms etc. So yes, in this example, a policy which said 'our club is not responsible for any members who take children underground' would help!
But again, what protects everyone the best is common sense - parents don't let their kids underground with people they don't trust, family friends don't take kids underground less they trust the kids and their parents.
And you know what? The whole thing is pretty sad, that we even have to consider it nowadays