  The Bardeen and Hayward spacetimes are here considered as standard
configurations of spherically symmetric regular black holes. Assuming the
thermodynamics of such objects to be analogous to standard black holes, we
compute the island formula in the regime of small topological charge and large
vacuum energy, respectively for Bardeen and Hayward spacetimes. Late and
early-time domains are separately discussed, with particular emphasis on the
island formations. We single out conditions under which it is not possible to
find out islands at early-times and how our findings depart from the standard
Schwarzschild case. Motivated by the fact that those configurations extend
Reissner-Nordstr\"{o}m and Schwarzschild-de Sitter metrics through the
inclusion of regularity behavior at $r=0$, we show how the effect of regularity
induces modifications on the overall entanglement entropy. Finally, the Page
time is also computed, showing its asymptotic behavior. Specifically, the Page
time exhibits slight departures with respect to the Schwarzschild case, more
evident in the Hayward metric only. Conversely, our findings on Page time show
that the Bardeen regular black hole is quite indistinguishable from the
Schwarzschild case.
