We report on first proof-of-principles results on non-sequential double ionization of argon and neon achieved by using a newly developed long-cavity Ti:sapphire femtosecond oscillator with a pulse duration of 45 fs and a repetition of 6.2 MHz combined with a dedicated reaction microscope. Under optimized experimental conditions, peak intensities larger than 2.310(14) W/cm(2) have been achieved. Ion momentum distributions were recorded for both rare gases and show significantly different features for single as well as for double ionization. For single ionization of neon a spike of zero-momentum electrons is found when decreasing the laser intensity towards the lowest ionization rate we can measure which is attributed to a non-resonant ionization channel. As to double ionization, the longitudinal momentum distribution for Ne(2+) displays a clear double-hump structure whereas this feature is found to be smoothened out with a maximum at zero momentum for Ar(2+).