This is where the rain from your roof discharges into an
internal channel. As a general rule, in construction this is not best practice,
however it is sometimes unavoidable.
If you are forced in this direction, the best option is to line the gutter in copper and solder all the joints. This can come at considerable cost and is therefore not generally feasible for most people.
The next best option is one continuous role of Butynol that encompasses the full length and width of the area where water will be present.
Failing the previous options, then a torch-on membrane approach can be used, normally with Bitumen. Your Local Plumber do not recommend this as it inevitably becomes brittle with age and will crack.
Often people suggest using a waterproofing product, however we have also found these to be ineffectual in the long run. The end result is always a leak that is difficult to find and, at worst, hidden until the internal damage becomes so great major repair work is required.
As a worst case Coloursteel can be used. Yes this is cheap, but tin rusts out and the silicone joints will give way. As with the membrane approach, damage will generally not be noticed until major repair work is required.