Well, even if you do have savings and your dh was laid off, you could still exhaust your savings. So having savings or not is one thing but worrying about it is a choice.
You are worrying about something that hasn't happened and something you have little control over. That is borderline neurotic. So yes, YABU for worrying A LOT about it, rather than taking little steps to have savings. @ourblanche has a great idea.
If you don't have debt, then you are actually better off than many other people who have no savings and only debt!
You are worrying about something that I have been through.
We went from having a big house, and £20k of savings through to 22 months of unemployment - we lost ALL our savings and finally had to sell the house (due to imminent foreclosure) - after paying debts - ZERO left over.
Dh was fortunate to get a job just as we found a buyer for the house. We moved cities and had to borrow more money from family to pay deposit for rent and for the move. Because we moved nearer London and rent is so high (50% salary) - we have hardly any ability to save. We are now renting without any foreseeable opportunity to save for a deposit to own a house.
Dh worried about it all the time. He is still worried we have only been able to save £800 in 15 months. Me - I had faith that things would turn out ok. I am a Christian, and my faith just got me through it. I honestly didn't worry about it and still don't. My security is not in cash - I have seen it can be gone in a flash. I have seen all the good worrying has done to dh -what a waste of energy. What will happen will happen whether you worry about it or not.
There are worse things than being poor due to lack of savings. It is uncomfortable and if you have the ability to avoid being poor - great, but if it is unavoidable, at least being poor in the UK is better than many other places I can think of.