Hi Crazee Cat
I work from home most of the time now. My employer (a major bank) is happy for people to work from home, as it’s cheaper for them. And it doesn’t actually matter that much, as half my team are elsewhere in the country, and most of the people I deal with are in India (that makes my job sound far more exciting than it is!). Every company will be different, but you’re best off speaking to your manager and HR department. The fact you already do it one day a week works in your favour, so they may be more open to increasing it. It might be worth speaking to your union rep if you have one.
I’d also get in touch with Access to Work. It’s a DWP thing to help people with disabilities to stay in work, giving advice on things that would help, and can also provide the funding (they pay for my taxi to & from the office when I do go in).