The mismatch between direct measurements of the current expansion rate of the Universe and the $\Lambda$CDM prediction based on early Universe observables (the so-called Hubble tension) has motivated the search for new physics that can accommodate these measurements. Here we discuss a possible modification of standard cosmology at energies between Big Bang Nucleosynthesis and recombination that does not spoil the fit to Cosmic Microwave Background measurements in a significant way, while injecting energy to boost the expansion rate. The mechanism is based on the existence on a scalar field, the majoron, which is motivated by particle physics models attempting to explain the origin of neutrino masses, and has been proposed as a possible solution of the Hubble tension. Here we expand that model to make this majoron an axion-like particle, linking the production of this particle to the primordial magnetic field.