Depends on how it's implemented. £100 billion is a lot but if the costs are spread out over time then it isn't necessarily so bad. Perhaps the better thing to do rather than wipe out all student debt is to just adjust the repayment terms, say by writing off the loan earlier. For post-2012 students I think it's 30-35 years they have to repay (if earning over £21k), whereas for pre-2012 students it's something closer to 25 years (variable). Perhaps, rather than write off all debt, you could just realign the two schemes and have post-2012 students only paying back for 25 years. Or you change the threshold for repayment upwards, say by insisting that students only repay if you have a salary that's above the national average?
Wiping it all out in one stroke is clearly not an option. I'm not saying that the two suggestions above would work either. The second one would be my preference since it's targeted at the lower end of the income scale.
But still, as has been pointed out, much of the student loan cost is never recuperated anyway. On its own that's enough reason to look again at how loans are managed. What is the point of saddling students with such significant debts, which does have some psychological impact, if you aren't expecting them to repay the debts? Even if you still hold by the principle that students should be the ones to pay for their university education, and that's not exactly an unreasonable principle, then you should still want the current system to be looked at again. It's not really working.