We present B q → ρ, B q → ω, B q → K ∗, B s → K ∗ and B s → ϕ form factors from light-cone sum rules (LCSR) at O(αs) for twist-2 and 3 and O(α0s) for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-4 (and 5) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for B → K ∗ℓℓ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low q 2 as well as combined fits to LCSR and lattice results covering the entire kinematic range for B q → K ∗, B s → K ∗ and B s → ϕ. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for B → K ∗γ as well as B → K ∗ℓ+ℓ− and B s → ϕμ + μ − at low dilepton invariant mass. Employing our B → (ρ,ω) form factor results we extract the CKM element |V ub| from the semileptonic decays B → (ρ, ω)ℓν and find good agreement with other exclusive determinations.