We present a new method to reconstruct the solar spectrum irradiance in the Ly α – 400 nm region, and its variability, based on the Mg ii index and neutron-monitor measurements. Measurements of the solar spectral irradiance available in the literature have been made with different instruments at different times and different spectral ranges. However, climate studies require harmonised data sets. This new approach has the advantage of being independent of the absolute calibration and aging of the instruments. First, the Mg ii index is derived using solar spectra from Ly α (121 nm) to 410 nm measured from 1978 to 2010 by several space missions. The variability of the spectra with respect to a chosen reference spectrum as a function of time and wavelength is scaled to the derived Mg ii index. The set of coefficients expressing the spectral variability can be applied to the chosen reference spectrum to reconstruct the solar spectra within a given time frame or Mg ii index values. The accuracy of this method is estimated using two approaches: direct comparison with particular cases where solar spectra are available from independent measurements, and calculating the standard deviation between the measured spectra and their reconstruction. From direct comparisons with measurements we obtain an accuracy of about 1 to 2%, which degrades towards Ly α. In a further step, we extend our solar spectral-irradiance reconstruction back to the Maunder Minimum introducing the relationship between the Mg ii index and the neutron-monitor data. Consistent measurements of the Mg ii index are not available prior to 1978. However, we remark that over the last three solar cycles, the Mg ii index shows strong correlation with the modulation potential determined from the neutron-monitor data. Assuming that this correlation can be applied to the past, we reconstruct the Mg ii index from the modulation potential back to the Maunder Minimum, and obtain the corresponding solar spectral-irradiance reconstruction back to that period. As there is no direct measurement of the spectral irradiance for this period we discuss this methodology in light of the other proposed approaches available in the literature. The use of the cosmogenic-isotope data provides a major advantage: it provides information about solar activity over several thousands years. Using technology of today, we can calibrate the solar irradiance against activity and thus reconstruct it for the times when cosmogenic-isotope data are available. This calibration can be re-assessed at any time, if necessary.