Is $600/week enough to live comfortably in London? It’s not enough to live comfortably in most large cities in the US. Our mortgage payment is $2200/month. And we live in the most affordable large city on the West Coast (Portland, Oregon). LA, SF, and Seattle would all be much more.
If by we, you mean two people, then it's $1200/week for the both of you. So that leaves you $2600/month after housing (maybe not including taxes, utilities, repairs). That doesn't seem too bad.
Also, you're talking about a mortgage for a property worth over $400k. It's unreasonable to expect that unemployment would be enough to pay everyone's mortgage, regardless of how much it is.
Not everyone's spouse would automatically qualify for unemployment. For example, if I make enough to cover the $2600/month rent on my own and my wife is a full-time caregiver for our aging parents, if I lose my job we would only collect one unemployment check.
Yeah, if I were planning for that level of income, then we could probably comfortable cover our bills. My wife would have to already have a job. And we'd have a pretty sizable commute to get to work. So, bills would get covered, but life would be a lot less comfortable (though comfortable when compared to not being able to afford the basics).
But Portland is pretty affordable. $400k doesn't get you much in California (there are foreclosures in South Central listed for that much on Zillow right now).
