1. Child tax credit works on your previous year's income so it can take up to a year to get adjusted. Same with child benefit.
2. Housing benefit takes 8-12 weeks to come through. Not only that it won't cover most private rents inside the M25. The council waiting list is 3-5 years in London so you'll have to go into arrears. The only way out is to stop paying your rent and go the council and tell them you are homeless. At which point either you or your children are split up or you get wedged in what I can only describe as a "crackhead den" at best. My other half had to clean the needles away before she could wash in the morning when this happened to her (after she was made redundant and the market was suddenly saturated with her speciality).
3. You don't get JSA immediately. It takes 4-8 weeks for it to start.
You don't just clap your hands when you're unemployed and cash starts rolling in. There are other concerns.
It's a fucking rough ride and not only that you have to do the legwork and deal with government incompetence and prejudice along the way which is more than rife.