Thanks for the replies. Brian, the problem is not that the discharge is
overloading the gutter, it's that with a high cross-wind it's not even
reaching the gutter: it's blown away from it, to cascade off the side of the
roof, where there is no guttering.

I had wondered about some sort of clips, so Harry thanks for that; and the
thought of directing the flow with flashing is a good one too, so thanks
John.