"Brooks" tend to be so small that the names often don't make it onto a map. The stream near my village is known locally as "Cally Brook" but you won't find that on any map. It's likely to be under-represented in the study which is based on Ordnance Survey mapping data.

"Water of [somewhere]" is a typically Scottish construction, and widespread. I can't think off-hand of any south of the border, where as Ripov says it's more likely to be used for standing water rather than a river.

"Gill/ghyll" is common in the Lake District. "Bourne" is a southern variant of the northern "burn", although I think it's probably more often found as an element in the river's name (eg River Ingrebourne, which I grew up near) rather than a generic term.

As with other aspects of place-names, as the map of settlement names also show, these reflect how the British Isles were populated by different groups over the centuries.