With difficulty and constant vigilance.
That said, until the GBC I was earning approx £50-£60 a year with 3 kids, a stay-at-home wife, and I was constantly skint. I'd never really learned to 'manage' money properly and by consequence, I was struggling to tread water with all the debt I had.
Then came a nasty divorce, and to cut a long story short me filing for bankruptcy. Suddenly I was left without debt nor even access to my kids who by now lived overseas. I resolved to get a degree and went to Uni the year before fees tripled; I hope the degree would help me move to the country where my children now lived. Then, while I was doing my degree my ex-wife had a change of circumstances and sent the kids back to live with me in the UK.
I'm still at University, presently coming to the end of my doctorate. Our family is surviving on the budget you have outlined, broadly what you say for rent, utilities, and council tax. Income is a mixture of a university stipend, tax credits, teaching hours, child benefit and child support. I have no partner so we are a single income household.
To my great surprise, we are now coping far better than I ever was when I was earning twice what I earned now. I think that, when I was younger, thinking about money depressed me because I never had enough of it. Whereas now I have less money I am forced to think about it constantly, and by consequence of this constant reflection the disasters of "need money but no savings/credit cards maxed out" issues, that is to say, these little short-term emergencies don't happen as much. Because I am constantly looking ahead two, three, four weeks ahead of the present so as to anticipate these short-term liquidity issues. I think the new banking apps have really helped with this too in comparison to what was available 10 years ago.
I have friends who, having never had the personal lives blow up in the way mine did who remain as useless with money as I was then. One even now has his salary paid into his wife's account so he can't blow it on nonsense because he has to ask her first (personally I think this is treating his wife like his mum, but its none of my business). Whereas I, for the first time in my life and maybe a third of his personal income now have a fantastic credit record, virtually no credit card debt, and both short-term and long-term savings.
I guess what I am trying to say is an absolute value of say, £30K is not that helpful. Despite the disparities in living costs across the UK it all depends on how good an individual is with managing money and not getting into difficulties with it. It took me going bankrupt and suddenly trying to raise three children on an undergraduate income to learn how to do it, but do it I did, and I am very proud of that. I hope others wouldn't need to have to go through as much to get to that same place though.