This is probably obvious (given the article is in the Daily Fail), but just to be clear this is a very unrepresentative slice of London life. I do think there is a tiny subset of people like her who grew up in luxury when London "high society" was very largely British people with good professional jobs. They probably have seen their "cost of living" (if you include things like Chanel and holidaying in Monte Carlo) increase far faster than the rest of us due to globalisation and London becoming a world city.
However, saying you can't live a very luxurious lifestyle on £100k is totally crazy. Even after tax you would be left with £65k after income tax and NI. Let's say you would have £60k left after paying for "essentials" other than rent (local taxes and utilities, basic groceries and bus/tube travel and/or bike rental to/from work).
Now to rent. My last flat before we bought had a rent of £20k per annum (which I paid half of). That was a beautiful warehouse conversion with 2 beds, 2 baths, a huge living/dining/kitchen and views of the Thames to one side and over a pretty park surrounded by other Victorian warehouses on the other side. It was very peaceful, and close to some lovely old pubs on the Thames. I could walk to work in 25 minutes (taking in views of the Thames, Tower of London, and Leadenhall Market on the way).
Can you tell it was not really a hovel? Rents have gone up quite a bit since then (this was 2-3 years ago), but there is no question you could still get yourself a very nice flat for one person within walking distance of the city centre for £20k per annum. Personally I would never dream of spending that much solo, but each to their own.
So even if you decide you need a super-luxury flat that leaves you £40k for holidays, posh groceries, sandwiches, coffees, taxis, restaurants and savings.
If you can't get by on £100k and still save at least 20% for retirement and buy yourself the odd nice dinner or a fancy holiday once a year (if that's what floats your boat) then something is going very wrong... my guess is the £370 shoes gives the best clue to what that thing is...
I would also point out: she talks about her father never earning more than £130k per annum. Based on his wikipedia entry I would guess he hit his peak when he was working for NewsCorp in the mid 80s. £130k in 1985 is worth about £350k today. So she is earning around a quarter of what her father was: not so surprising then that she can't afford the same lifestyle!
http://en.wikipedia.org/wiki/Woodrow_WyattHaving said all that I quite enjoyed the article. The lady can write!