I've raised £10000 to to fund a powered wheelchair and other necessary equipment (e.g. hoist) for me to be able to get around independently and go to university

I don't qualify for a wheelchair on the NHS despite my physio, occupational therapist and rheumatologist (all of whom are from the NHS) all agreeing that I need one in order to be able to leave the house independently and go to university. I have been using a basic £100 manual wheelchair from amazon for the last couple of years. However, I can't self-propel and it's beginning to fall apart.
Recently, I turned 18 and while for most people this means greater independence, mine is greatly limited by the fact I do not have a powered wheelchair.
I have a permanent connective tissue disorder, as well as many other health conditions that will mean that I will require a liver transplant in the future. As it is, I am unable to walk without the use of aids such as crutches inside the house, but I rely on a wheelchair to be able to travel to my hospital appointments (most of which are in London).
Going to university is very important to me as I am very academic and want to study biomedical sciences to potentially go in to medical research as a career. However, I won't be able to achieve this without a wheelchair as I won't be able to complete day-to-day tasks such as buying food and getting to lectures.
Currently, I have been unable to leave the house independently for the last year and a half. This means that I can rarely go out to see friends or even choose my own clothes as I am reliant on my mum or other family members (such as my two younger sisters) to help get my wheelchair in and out of the car, as well as help me to push it since my joint condition prevents me from being able to self-propel.
We haven't been able to fund a powered wheelchair ourselves as my mum is a single-parent, self-employed and is studying to become a social worker - we're a little tight on funds!