The rest is true, but a absolutely major one that is missing in the UK is unemployment benefits. If you lose your job you basically have no income at all.
Not only that, they are not available to visa holders, contrarily to most first world countries.
Lastly, the amount is still laughable. In Luxembourg I would have had 80% of my salary for a year, without conditions. The UK is not a first world country at all.
Because Luxembourg has a contribution-based welfare state. The money you are being paid is your own money that is being returned to you by the state when certain conditions are met (and yes, if you look at any contribution-based system, there is heavily conditionality, universal systems are the only ones without conditionality). The UK annual benefit bill just for people of working age is larger than Luxembourg's GDP.
The UK has a universal system that everyone can access regardless of circumstances. You just don't understand how it works at all (this is quite typical, Brits do not understand contribution-based systems either because they are used to a system where the state pays out massive amounts of cash to people in excess of the amount they paid in).