I started a reply to this last night, but for a host of reasons didn't complete it, so I'm glad that others have brought up the ones that I would have, including RDA (riding for the disabled association). I suspect volunteering at a local stables, however useful, wouldn't count as that will be a for-profit organisation. The RDA are pretty much always looking for volunteers and ime are happy to take whatever you can give timewise, but due to large horses being involved, they might have an age limit, I'm not sure (it was never an issue when I was looking into it, I was well above any such limit...)
Depending on where in the Oxford area you are, there is St Tiggywinkles, which provides rescue and nurturing for hedgehogs who are ill or injured. I took one there a couple of years ago after I found him/her wandering around my driveway in full scorching sunshine at midday, clearly confused and going round in circles. It's on a lovely country lane, but may be a bit awkward to get to...
With other animal charities, I'd be tempted to try to support the little ones, the ones that don't have the national coverage and often are in someone's back yard, one-man bands that run on shoestring budgets with margins you couldn't thread a needle through. Where one person's help will make a huge difference, rather than being one of a host of volunteers. But it is of course going to depend on what's reachable for her to go regularly.
Sounds exciting, whatever she ends up doing!