Very nice find! I think the specimen would be worth professional preparation especially given a possible complete fish specimen.
Excerpt from 'Fossils of the Oxford Clay',1991,The palaeontological association,edited by David M. Martill and John D.Hudson.
Elongate fusiform fishes, external bones feebly ornamented. Teeth large
and evenly spaced on dentary, finer and closely spaced on maxilla, small
and densely distributed on inner bones. Well developed gular plate,
prominent branchiostegal rays. Caudal fin deeply forked.
Remarks. Caturus is probably the most common bony fish macro-fossil
encountered in the Oxford Clay.
Caturus porteri Rayner
Description. A caturid in which the depth of the dentary below the most
posterior tooth is one-quarter the length of the dentigerous border.
Teeth of the dentary fine, gently recurved, closely spaced. Gular plate
with prominent centre of ossification, 20 or more branchiostegal rays.
Range. Known from the Lower Oxford Clay of Peterborough and
Whittlesey, Cambridgeshire, Calvert, Oxfordshire, Milton Keynes,
Buckinghamshire, and Christian Malford, Wiltshire.
Description. A second species of Caturus is indicated by the presence of a
caturid-like dentary in which the depth of the dentary at the posterior
tooth is one-quarter the length of the dentigerous border as in C. porteri,
but where the teeth are evenly spaced, large, robust, slightly recurved
lingually, and with expanded roots.
Range. Only reported from the Oxford Clay of Whittlesey,
Cambridgeshire (Martill, 1985).