High quality electron beams have been produced in a laser-plasma accelerator driven by femtosecond laser pulses with a peak power of 26TW. Electrons are produced with an energy up to 150MeV from the 2mm gas jet accelerator and the measured rms relative energy spread is less than 1%. Shot-to-shot stability in the central energy is 3%. Pepper-pot measurements have shown that the normalized transverse emittance is similar to 1 pi mm mrad while the beam charge is in the range 2-10 pC. The generation of high quality electron beams is understood from simulations accounting for beam loading of the wakefield accelerating structure. Experiments and self-consistent simulations indicate that the beam peak current is several kiloamperes. Efficient transportation of the beam through an undulator is simulated and progress is being made towards the realization of a compact, high peak brilliance free-electron laser operating in the vacuum ultraviolet and soft x-ray wavelength ranges.