We have studied magnetic excitations in two single crystals of CuGeO3 doped with Ni2+, using inelastic neutron scattering at wave vectors close to the antiferromagnetic zone centre, Q=(0,1,1/2). Pure CuGeO3 is a one-dimensional compound with a spin-Peierls (S-P) gap of approximate to 1.95 meV. When Ni2+ is substituted for Cu2+ in CuGeO3, the 1D chains are broken into finite segments, suppressing the S-P phase and inducing a tow-temperature transition to coexistence with antiferromagnetic order. We show that for the 1.7% Ni-doped crystal the S-P gap is renormalised to approximate to 1.7 meV, while approximate doubling of the dopant concentration to 3.2% results in an almost complete collapse of this excitation. Instead, measurements on the 3.2% Ni-doped crystal revealed a magnetic excitation that could be clearly resolved from the elastic magnetic peak. This excitation followed the dispersion expected for the anisotropy gap in an antiferromagnet and comparison with an equivalent model of the S-P gap in CuGeO3 has yielded modified exchange coefficients. However, measurements could be made only for wave vectors close to (0,1,1/2) as the intensity declined rapidly with movement away from the zone centre.