I have just looked up the British Regional Geology Handbooks for Eastern England, Central England, and the Hampshire Basin. Each of these handbooks devotes more than ten pages to the Middle Jurassic, with lists of fossils (mostly marine invertebrates, with some plant fossils).
Also the book British Mesozoic Fossils (published by the Natural History Museum) describes the fossils of the Inferior Oolite ('rich in brachiopods and bivalve molluscs') and contemporary non-marine beds ('abound with fossil plants'), the Cornbrash Formation ('abundant brachiopods, bivalve molluscs, sea urchins and other fossils'), and the Oxford Clay Formation ('numerous ammonites', 'a wealth of vertebrate fossils, especially plesiosaurs and ichthyosaurs', 'coral reefs with their associated reef-dwelling assemblage of molluscs and sea urchins'). More than half of the book consists of drawings of Jurassic fossils.
None of these books mentions 'a global dearth of Middle Jurassic fossils', and the descriptions and drawings in the Regional Geology Handbooks and in British Mesozoic Fossils give no indication of any dearth of Middle Jurassic fossils in Britain.