What I will mention though is, reports like the one creeky gave a link to are written and back up by non witnesses, even the one in the report was no longer a witness so they will be very biased and do their uttmost to discredit the organisation.

Rather like many posters here

I accept that point but it really doesn't address my real worry.

What is the situation if a child or parent of a child approaches an elder to claim the child has been abused and the only witness to the act is the child and the accused abuser denies any abuse has taken place.  Would the Bible be followed and no further action taken or would the civil authorities be alerted so that they could investigate?

If the former then my opinion is quite simple - it is morally WRONG and repugnant.