Unless you live in central London, or go out boozing every weekend like a retard, you can get by and live comfortably on UK minimum wage. I was living alone for 3 years on min wage and never wanted for anything, now I'm living with a friend so we split the rent, both of us working just above the new min wage and money is literally the least of our worries.
Of course, if you're one of those idiots who spends £100 every weekend to get drunk and feel like shit in the morning, or gets an expensive car on finance and then realise you can't keep up with the payments, then you're gonna have worries. If you have at least a rudimentary spark of intelligence in your head minimum wage covers everything you need plus gives you a decent amount of disposable income.
Don't know where you pulled the "slave wage" idea from, or perhaps you're just being unnecessarily insulting, but most people get by just fine on min wage full time jobs in the UK.