After doing more research I've decided to stick with my original plan. The train direct between London and Edinburgh is only £23 (not £70 and no change at Glasgow as detailed above), and luggage sending services are £19 for a suitcase. I'm disabled so can only carry one small hand luggage sized suitcase on the train with me, so shipping is necessary if I want more than a weekends worth of clothes.
A lot of the advice above doesn't apply to my situation. I'm not taking up bedding, towels, pots and pans etc as all of that is being provided by my accommodation. The only thing I'm taking is my clothes and books. I'm not re-buying things I already own as this will cost far more than simply shipping stuff up there. I'll buy toiletries and things up there. I'm not moving into halls and I'm coming from my own flat, not a parents house. I won't be "coming home" in the holidays like younger students would, so need to make sure I have everything I need.
Thanks for all the info folks! Although it wasn't helpful for me, it might be for someone else reading this. Cheers!