I would look at the true state of the alternatives before panicking. It may be that it isn't anywhere near as bad as you're imagining.
A girl in my youngest son's class joined the school last year from a private school. Her mum had always planned to take her out at secondary school time, because our secondary schools are so good, but financial pressures meant she had to do this much sooner than planned.
She now says it's the best thing she could have done, for both her older daughter and the youngest who has just started school, and wishes she'd done it years ago!
It really is melodramatic for your husband to say he'd rather die than take them out of the private sector.
Take a deep breath, and a good long look at all your options. Look at all the state schools which are practical from where you live. Go and see them in person, get a feel for them.
Be open-minded and don't pre-judge schools beforehand. For example, you say one child needs a small and intimate school, but my children are in a big-ish school which still retains a lovely family feel to it. Every school is different, so approach each one in a fresh way.
If staying private matters that much to you, then perhaps consider some of the options Xenia mentioned, but also consider the impact these could have on family life (if you take in a lodger or go back to full-time work), or on your longer-term finances (if you remortgage). Speaking personally, I would say none of these options would be worthwhile just to keep your children in a private school, but then I'm not you and I don't have the same concerns or priorities.
It would be a change for your children, there's no denying it, but it needn't be a negative one. And it sounds from your posts like it may not even come to that. But if it does, make sure the children don't pick up on any negative feelings - it's better if it's presented in a matter of fact way as a normal or desirable thing, or even an exciting thing!