The situation with blanket peat moorland is slightly more complicated than the description in your article, but there is a strong core of truth. The big issue is with historical gripping (drains) which sends the water off the moor as quickly as possible to promote heather at the expense of other species, however the old canard of peat being like a sponge isn't quite the case either- peat in many ways behaves like concrete, with water running straight off. Healthy peat has very low hydraulic conductivity- most of the apparent absorbsion is via pipes, or underground cracks in degraded peat. To reduce or attenuate those destructive spikes in flood hydrographs, stopping the intensive management of grouse moors is a start, but needs to be coupled with other changes in management, such as removal of sheep in favour of lower intensity grazing or the cessation of grazing alltogether to promote a larger vegetation structure including scrub and trees, particularly downslope away from the peat dome. This will slow down runoff, hopefully removing the damaging extreme spikes - higher river levels for longer, but without the damaging short term extreme flows.
However, extreme events are just that, and these measures need to be coupled with both engineering solutions and a re-evaluation of how and where we build, but that requires a change in attitude by planners, house builders and most importantly the prospective inhabitants.