@Multiplicationarithmetic
Good on you for deciding to divorce him! As far as what it's like living in the same house during the 'legalities', I'd say it depends on the people and the house.
If the couple agrees they're better apart and there's room enough, I suppose they agree to 'ground rules' and begin to live as roommates. They start dividing up domestic chores, figuring out how to divide the household expenses. And what the 'living arrangements' are going to be (ie someone moves to the spare room or in with a child).
If it's a 'one-sided' divorce well, I suppose it can be anything from just 'uncomfortable' to hell on Earth. If the house isn't big enough for a spare room or sleeping in with a child, then the one who wants 'out' may have to sleep on the couch. Finances can be difficult if the one who wants out isn't financially 'independent' as the other person may refuse to pay more than what it takes to keep the household running, if that. There is no counting on them giving you any money at all for your own needs. If there is violence or abuse, well, it continues until you can get out or it rises to the level where the police get involved and you can get an Occupation Order &/or Non-molestation Order.
The optimum is to find a safe place to go, get out, then file for divorce. Is there nowhere you can go? I'd go to a shelter or sleep on someone's floor in order to get out.
Depending on what you told the solicitor about leaving, the solicitor may just be being realistic about having to stay through the proceedings. It may be that they were trying to explain to you that your H will NOT have to pay your living expenses once you leave. Yes, he'd have to pay child maintenance, but that alone is rarely enough to rent a flat and pay the bills. I don't know what benefits you might be entitled to (I'm not in the UK).
So yes, there are obstacles and things will be, well, 'not nice' for awhile. But in the end you will be free. And that's worth the discomfort.