The invention relates to a method for the hydrocracking of at least one hydrocarbon feedstock, of which at least 50 wt.-% of the compounds have an initial boiling point above 340 DEG C and a final boiling point below 540 DEG C, using a catalyst comprising, in the oxide form thereof, at least one metal selected from the group VIB metals, the group VIII metals and the group VB metals of the periodic table, alone or in a mixture, said metals being present in the form of at least one polyoxometalate having formula (HhXxMmOy)q-,wherein: X is an element selected from among phosphorus (P), silicon (Si), boron (B), nickel (Ni) and cobalt (Co), said element being taken alone; M is one or more elements selected from among vanadium (V), niobium (Nb), tantalum (Ta), molybdenum (Mo), tungsten (W), nickel (Ni) and cobalt (Co); O is oxygen; H is hydrogen; h is an integer between 0 and 12; x is an integer between 0 and 4; m is an integer equal to 5, 6, 7, 8, 9, 10, 11, 12 and 18; y is an integer between 17 and 72; and q is an integer between 1 and 20, said polyoxometalates being present inside an oxide-based mesostructured matrix of at least one element Y selected from the group containing silicon, aluminium, titanium, zirconium, gallium and cerium and the mixture of at least one of said elements. The matrix has a pore size between 1.5 and 50 nm and amorphous walls with a thickness of between 1 and 30 nm, and the catalyst is sulphurised prior to use in said method.