Headwater blanket-peat restoration activities, in particular revegetation and gully-blocking, are observed to deliver significant Natural Flood Management (NFM) benefits. A recent Before-After-Control-Intervention (BACI) experiment showed that these interventions reduce flood-peaks and increase lag-times, but the processes controlling these effects remain unclear. We seek to identify these processes at the same BACI sites by inverting the TOPMODEL rainfall-runoff model and linking the response-to-intervention in each catchment to model parameters through rigorous calibration. Through numerical experiments, we infer processes most likely to be driving the BACI observations. Our findings confirm the NFM benefits of these restoration-focused interventions. Independent of storm size/intervention, the increased lag is almost entirely due to surface roughness reducing the floodwave speed. We conceptualise this as a ‘mobile’ surface storage. In flood-relevant storms, at least 90\% of the peak reduction in both interventions is delivered by mobile storage. The additional increase in the mobile storage due to gully-blocking is very significant and comparable to that of revegetation alone. The impact of interventions on ‘immobile’ storage (interception+ponding+evapotranspiration) becomes important for smaller storms, in which revegetation reduces peak discharge by increasing evapotranspiration but the not interception storage. Gully blocking however, increases ponding but reduces evaporation, such that there is no net gain in catchment immobile storage relative to revegetation alone. Although interventions always increase lag-times, they can be less effective in reducing peak magnitude in long duration frontal rainfalls. We propose two approaches to further increase catchment’s surface storage, while adhering to the restoration requirement to keep the water tables high.