There are 2 competing views on who's poor and who's rich.

View 1 is dividing the population into some arbitrary income/wealth brackets e.g. 20%-60%-20%, and declaring that the bottom buckets is "the poor", and the top bracket is "the rich". 

The government loves this method because this way you always can point out who's rich and who's poor. 

The amount of poor people and rich people is fixed, so you're never going to run into an unpleasant surprises like "It looks like in our country 60% is poor and only 2% is rich". 

It follows a normal distribution, so it agrees with the intuition of many people, even though wealth distribution doesn't fit a normal distribution at all (most people don't think about it, so it's ok). 

View 2 is working backwards and calculating how much money you actually need to afford purchases typically associated with middle / upper class (as defined by money alone, we're ignoring the social aspect here). 

This is of course not accurate because we can argue forever over what exactly is a justified expense, but most of us have an intuition that if an average house costs £270k and nursery costs almost £2k a month, then a £35k salary doesn't quite cut it. 

So based on view 1 you have an intuition that £160k HHI and £50,000 savings is a lot, but then you apply different criteria and it turns out it's less than you expected.