Robby, how on earth can walking out without saying anything be a health and safety matter?
On the other hand, you can be dismissed for your perceived behaviour. It depends very much on company policy.
You have two options as I see it:
A) You can fight. Keep calm about it, log everything, keep evidence and don't give in. Ultimately you can take him to a tribunal if you believe you have been unfairly dismissed.
B) Don't try to go back. I know you probably need the money and you'll be strapped for a while. You'll maybe need to make a few temporary changes to your lifestyle, but what's the worst that can happen? It won't kill you, that's for sure. And the best of it is you won't have the stress, won't have a nervous breakdown.
I walked out on my employer eight years ago without another job to go to and it was the most liberating thing I've ever done. For all the worry about finding work, I was working again within a week of leaving. Does wonders for your confidence, I can tell you, knowing that you're not afraid to do it.
Even if you leave, still chase for unfair dismissal. You have nothing to lose and you may even get some money out them.