Laser irradiation of solid targets can drive short and high-charge relativistic electron bunches over micron-scale acceleration gradients. However, for a long time, this technique was not considered a viable means of electron acceleration due to the large intrinsic divergence (～50° half-angle) of the electrons. Recently, a reduction in this divergence to 10°–20° half-angle has been obtained, using plasma-based magnetic fields or very high contrast laser pulses to extract the electrons into the vacuum. Here we show that we can further improve the electron beam collimation, down to ～1.5° half-angle, of a high-charge (6 nC) beam, and in a highly reproducible manner, while using standard stand-alone 100 TW-class laser pulses. This is obtained by embedding the laser-target interaction in an external, large-scale (cm), homogeneous, extremely stable, and high-strength (20 T) magnetic field that is independent of the laser. With upcoming multi-PW, high repetition-rate lasers, this technique opens the door to achieving even higher charges (>100 nC).