The second order phase transition in a Heisenberg ferromagnet is studied where, in addition to the dominant short-range exchange interaction, dipolar interaction and a uniaxial anisotropy are present. Due to the competition of the three types of interaction which differ in symmetry and range, the critical region is characterized by crossover transitions between four nontrivial fixed points (Heisenberg, Ising, uniaxial dipolar, and isotropic dipolar). These transitions are discussed within the frame work of phenomenological crossover theory, and a effective Hamiltonian is derived which allows to set up the Gaussian model for the problem. The bulk of the paper is deidicated to the calculation of the Kouvel-Fisher effective exponent γ_eff to the one-loop order of renormalized field theory. The Є-expansion with Є = 4-d and the method of generalized minimal subtraction invented by Amit & Goldschmidt are applied. The effective exponent γ_eff provides for a detailed insight into the structure of the critical region and makes possible the interpretation of recent experimental data obtained for gadolinium and the compounds Fe₁₄Nd₂B and Fe₁₄Y₂B. The cases of isotropic dipolar ferromagnets and of dipolar Ising ferromagnets are included as limiting cases of the present study.