Further clarification may help: at present it appears that the situation is this:
You've got a club which organises trips
Non-members who are uninsured routinely join in on trips
If this is the case then the following observations arise (subject to input from an insurance expert):
If a club member gets injured as a result of negligence by an uninsured non-member there's no recourse* to a tidy sum to help with the aftermath, e.g. if the club member becomes paralysed his family will potentially be left destitute. (* Other than to pursue the club itself for recompense for negligence by allowing uninsured non-members to participate, perhaps).
If a non-club member gets injured as a result of negligence by an insured member then they'd perhaps get a pay out from insurers.
If a non-club member gets injured as a result of negligence by an uninsured non-member, because they were joining in on a club-organised trip they'd perhaps get a pay out from the club, or its officers.
If this is an accurate summary of affairs then it would appear that your club is taking a risk that it might have to pick up the pieces in the event of one of these uninsured non-members making a mistake whereas the uninsured non-members are nicely covered, courtesy of your club or its officers, in other scenarios.
If membership and/or insurance is a stipulation of access then by allowing hangers on, the club also appears to be failing to observe protocol in that regard.
Also it's probably fair to say that, if this is a reasonable summary of the circumstances, your club is habitually engaged in neglecting its duty of care to its paid up members.
Perhaps the club and its officers should guard against the risk of claims against them by the simple expedient of paying for the impoverished keenies to become BCA members and provide them with free membership; it could be much cheaper doing this than just crossing your fingers.