The problem might not be the brush.
I’ve never used the Cotman brushes so I’m not sure where they fall on the spectrum. It might help if you identify what the exact problem is – i.e. is it that the brush goes limp, it releases all the water at once, the paint is uncontrollable flowing everywhere, or the color is too light? Or something else?
If the color is too light it might not be too much water, it could be that the paints are not well pigmented. Cotman is a student brand so that’s possible.
If the brush goes limp – that’s something that softer brushes do. In some techniques, like Chinese brush painting, it is expected and used. The fix there is definitely a different, stiff brush, though not too stiff.
With many brushes, the problem is not that they take up too much water, but that they release it all at once. That isn’t so much a matter of soft or stiff as the shape of the individual bristles. A different brush is called for. A professional brush is less likely to have the problem but may (or may not) cost more.
The paint flowing everywhere can occur from several causes – too much water, uneven release as discussed above, the paper, or the pigment. Some colors, such a Phthalo Blue tend to be explosive and require careful handling. Others, such as Cobalt Blue have less movement and give you more control (but are granulating so you get darker dots of color). It can be the paint itself. The formulation may result in colors that go crazy.