Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can reach many kA peak current, over short distances. Space charge issues, even in transport lines as simple as a drift section, have to be carefully taken into account since they can degrade the beam quality, preventing any further application of such electron beams. We analyse the space charge effects within an electron bunch with numerical simulations in order to assess their effect on the beam. We use LPA beam parameters published in previous experimental studies. These studies can give an indication of the working point where space charge can dominate the beam dynamics and has to be taken into account in the application of such beams.