I tried searching for this, seems like a difficult question to search for. Take two examples, (one admittedly from a fiction but still accurate I would think). I seem to remember my grandad told me he got paid £5 a week in ww2 for being a messenger, this comes to about £600 a month in today's value. Then in a tv series I was watching called peaky blinders (based in 1920s), the main character offers his secretary £8 4 shillings a month. This comes to about £250 a month today. I guess the £600 a month could just about scrape by with basically no spare money, but the second example doesn't seem possible. Am I missing something?
I think your maths may be off. According to this site, £5/week in 1940 would be closer to £1200/month today.
Keep in mind that inflation is sort of an average, and doesn't reflect the changing ratio of the cost of things. In 1940, the largest monthly expense for a family was food. Today, it tends to be housing. (Back then, food was more scarce, and housing more plentiful relative to the population.)
Your grandad probably didn't own a telephone, telly, or car, only had three or four sets of clothing (at most), and lived in a shared flat. His costs of living were probably very manageable even on £14k/year.