Several groups are carrying out experiments to observe and measure vacuum magnetic birefringence, predicted by quantum electrodynamics (QED). We have started running the new PVLAS apparatus installed in Ferrara, Italy, and have measured a noise floor value for the unitary field magnetic birefringence of vacuum $\mathrm{\Delta }{n}_u^{(\mathrm{vac})}=(4\pm 20)\times 10^{-23}{\mathrm{T}}^{-2}$ (the error represents a $1\sigma$ deviation). This measurement is compatible with zero and hence represents a new limit on vacuum magnetic birefringence deriving from nonlinear electrodynamics. This result reduces to a factor of 50 the gap to be overcome to measure for the first time the value of $\mathrm{\Delta }{n}_u^{(\mathrm{vac},\mathrm{QED})}$ predicted by QED: $\mathrm{\Delta }{n}_u^{(\mathrm{vac},\mathrm{QED})}=4\times {10}^{-24}{\mathrm{T}}^{-2}$. These birefringence measurements also yield improved model-independent bounds on the coupling constant of axion-like particles to two photons, for masses greater than 1 meV, along with a factor-2 improvement of the fractional charge limit on millicharged particles (fermions and scalars), including neutrinos.