This paper presents a search for Higgs bosons decaying to four leptons, either electrons or muons, via one or two light exotic gauge bosons Zd, H→ZZd→4ℓ or H→ZdZd→4ℓ. The search was performed using pp collision data corresponding to an integrated luminosity of about 20  fb−1 at the center-of-mass energy of s√=8  TeV recorded with the ATLAS detector at the Large Hadron Collider. The observed data are well described by the Standard Model prediction. Upper bounds on the branching ratio of H→ZZd→4ℓ and on the kinetic mixing parameter between the Zd and the Standard Model hypercharge gauge boson are set in the range (1–9)×10−5 and (4–17)×10−2 respectively, at 95% confidence level assuming the Standard Model branching ratio of H→ZZ∗→4ℓ, for Zd masses between 15 and 55 GeV. Upper bounds on the effective mass mixing parameter between the Z and the Zd are also set using the branching ratio limits in the H→ZZd→4ℓ search, and are in the range (1.5–8.7)×10−4 for 15<mZd<35  GeV. Upper bounds on the branching ratio of H→ZdZd→4ℓ and on the Higgs portal coupling parameter, controlling the strength of the coupling of the Higgs boson to dark vector bosons are set in the range (2–3)×10−5 and (1–10)×10−4 respectively, at 95% confidence level assuming the Standard Model Higgs boson production cross sections, for Zd masses between 15 and 60 GeV.