Tungstate, exchanged on a (Ni,Al) layered double hydroxide, is applied as a heterogeneous catalyst in the oxidation of bromide with H2O2 and the ensuing electrophilic bromination of olefins. The high halogenation activity of the catalyst in essentially neutral conditions mimicks the activity of V-bromoperoxidase enzymes. In water, aromatic and aliphatic olefins are selectively converted to bromohydrins; in methanol, methoxybromides are produced. In appropriate solvent conditions, the bromohydroxylation of geminally di-, tri-, and tetrasubstituted olefins proceeds via dehydrobromination to the epoxide. Evidence for this mechanism is provided by kinetic and labeling experiments. This one-pot alternative for the two-step halohydrin epoxidation process is enabled by the mild pH conditions: bromide is effective in substoichiometric, catalytic amounts. All new catalytic procedures are characterized by a high oxidative stability of the catalyst, high productivity of the catalyst on weight basis, high W turnover frequencies in ambient conditions (up to 50 mol of product per W per h), and high chemo-, regio-, and stereoselectivities.