So as others have said..
She needs to outright ASK (insist) on a referral to Wheelchair Services.
Depending on where you are, that could be a fair wait (I was referred again in december. I am still waiting, I have a chair but it does not fully meet my needs now, I am hurting myself further continuing to use it, which they know...)...
Then, again depending on where you are, the wheelchair may only be provided in specific circumstances... and it ISN'T down to 'need', its usually whether you will use it to access work or education - if she is doing neither then certainly in my area, she would not get.
This is for manual chairs - for a powerchair she would need to demonstrate she has to use it inside the house, as well as the requirement for work/education (again, here, Worcestershire, other areas may have different rules).
The reality is, she could if referred NOW, be waiting 18 months to see wheelchair services, only to be told that if she only needs to chair to go shopping/socialising and if she cannot use it indoors (say, house too small), she can't have one...
So in all honesty, whilst I would ask for the referral... I would take her to somewhere good like RGK in Stafford, and get her a suitable chair made for her. RGK (and other wheelchair specialists, NOT mobility shops, but people who MAKE these chairs, custom) will find out her needs, take exact measurements and build a chair to suit her.
They aren't cheap, mine was 2.5K however it has kept me mobile for 5 years now.
Yes if you buy the chair either wiht an NHS voucher or entirely by yourself you are responsible for the maintenance... but if you effectively borrow an NHS chair, you will likely end up with something that doesnt meet her needs, breaks a lot, they take ages to fix them too..
Oh and the idea that the NHS will measure up and provide a suitable chair.. is hysterical. The one they wanted me to have i couldnt try in my size... i could not MOVE it myself it was too heavy and clunky and did not fit. Their plan was to order one in my seat size and id have it delivered and if it did not fit..... tough luck!