"Universal credit" is an administrative project to coordinate all the existing systems. The disability payments you linked to are subject to increasingly stringent processes which end up declaring terminally ill or permanently severely disabled people "fit to work" and withdrawing the funds they need to survive. This has resulted in some poverty-related deaths and suicides.

Jobseekers' allowance is also subject to heavy scrutiny. I've heard that the best strategy if you have children is to declare yourself self-employed on a zero-hours basis: this stops the jobcentre from hassling you as you no longer count as "unemployed", you just don't have any work. You can then claim "working family tax credits", housing benefit, and child benefit.