OP, I get it, I really do.
There's a total difference between being entirely alone and having someone in the house, even in another room, even for a set period of time.
My husband and I both have jobs that sometimes require flexible working (e.g. not M-F 9-5). I would luxuriate with the quiet on the days when he was in his office and I was at home. It's the feeling of uninterrupted quiet time to do exactly what I wanted to do--felt like kind of the mental equivalent to very clean sheets on a nice hotel bed.
Then covid came. We both worked from home full time, at least in the fall (we're in the States right now, though we're British). We were lucky enough to be able to build my husband a studio shed in the backyard, so that he worked outside and I worked inside.
It kept us from feeling totally suffocated. But it didn't create that airy, light, I get to do whatever I want feeling. He'd come in every couple hours to go the loo or grab lunch or ask a question, and while I love him madly and he was very good about not interrupting, I didn't feel like I could totally focus (and certainly didn't feel like my time was completely my own).
When offices opened up partially in the spring, I spent the first full day of him (and everyone else) out of the house in a kind of stunned happiness.
Again, I love him madly, he works in his studio, and he's not a pest. And still it wasn't the same.
So I get it. I really, really do. That said, I think the situation you have is not tenable for the long run. I know you don't want solutions, but you'll be miserable if things continue as they do. You need privacy, and it's worth paying for.
And here's the thing: it's really cheap right now. Some of the London agencies are doing free office space for the summer. You can get a private office in most big cities outside of London for under £300/month right now. This isn't a hotdesk or a shared space--it's a private office, with a door and with internet capabilities. Even the ones with dedicated desks (so, have locked drawers, etc.) have private phone booths for confidential conversations.
It's not great for him to exist entirely out of the home, either. I assume he has to clear up his mess every night, and transform his office back into your dining room/sitting room/whatever, and that can't be fun.
In sum, I think it's really, really shitty that businesses have decided to go full wfh. I know there are some on this board who love it, but I think it's just passing on the expenses of working (space, privacy, tech, etc.) onto the worker. And his/her family.