The writer of the article could easily be able to save £400 - £600 pcm. That would very quickly add up.
Not to a house deposit in London, it wouldn't SciFiFan.
Saving e.g. 500 pounds per month for 5 years would only add up to 30,000 which is not enough for a deposit on a London property or anywhere close to London, really.
All this 'look after the pennies and the pounds will look after themselves' stuff is crap. You can live like that but it's incredibly hard and depressing. DH and I lived like that for 7 years, scrimping along for a house deposit, renting a tiny, damp flat, eating 99p cans of soup for lunch and making giant lasagnas on the weekend to last for meals for the week instead of eating out. It was fucking miserable and at the end of the time, yes, we had paid for our own wedding and also had a 30k deposit for a house but we were only able to buy because we were in Scotland.
What really changed our lives was upping our income. Or rather DH's income who was offered a job in the US a few years ago and has progessed in his career to the point where he is now earning exceptionally well.
We worked incredibly hard in the UK and saved and were 'sensible' and now I look back at my 20s and think what a waste it was. All I learned is that the global economic system is rigged against working people and the only way to escape it is to make sure you become a 1%-er yourself. Rich people know this already which is why they get jobs in the City and leverage money to make money. You can bet they don't scrimp on small luxuries to afford a basic human right because they don't need to. They will lecture that nonsense to the masses, however, to keep us dreaming big.
I recommend 'Pound Foolish' a book by Helaine Olen that exposes the myth of the personal finance industry and how it has conned people into thinking they are in charge of their own financial destiny at a time when wages are stagnating and working people are under siege from all kinds of economic forces that increase income inequality. It is focused on the US where consumer regulation is weaker than in the UK but very insightful.