Gamma-ray angular distribution measurements following the natNi(n,n′γ) reaction were carried out at 1.6 and 1.8 MeV neutron energies. Through the Doppler-shift attenuation method, the lifetime of the 2+1 state in Ni58 is determined as τ=1.00+0.15−0.10 ps, which yields a B(E2;2+1→0+1) value of 9.4+1.0−1.2 W.u. From previous measurements and this work, average values of τ=0.94(3) ps and B(E2;2+1→0+1)=10.0(4) W.u. are recommended as standards for normalization. In addition, a longer lifetime of τ=1.30+0.30−0.20 ps has been determined for the 2+1 state in Ni60, which yields an E2 strength of 10.7+1.7−2.5 W.u. Our results support an enhancement of proton-core excitations and related quadrupole and pairing strengths in the light Ni isotopes, in agreement with mean-field and shell-model calculations.