The out of copyright 1974 (1:2,500) OS map has the Wye extending further north west than the relation, although they seem to be missing a tile/sheet & it's possible the waterways have changed course due to mills no longer needing the volume of water they needed (Verco have made furniture here since 1932)

National Library of Scotland map viewer: https://maps.nls.uk/geo/explore/side-by-side/#zoom=16.8&lat=51.64237&lon=-0.79941&layers=258&right=osm

relation: https://www.openstreetmap.org/relation/12432638#map=15/51.64248/-0.79269

It also has the waterway between here (https://www.openstreetmap.org/way/610284448 ) and the end of Desborough rec ground (https://www.openstreetmap.org/way/26995603 ) as being the Wye.
