In the context, this is probably correct.
However it is also government peddled rubbish as well.
To Calculate the true tax on earnings, add 13.8% of your gross pay to the NI contributions.
i.e. at £40k (using Saracens figures above) you pay £9845(combined Tax and employees NI)+£5520 (employers NI)
So your £45520 pay - Not the £40,000 you think you earn - you Pay £15365 in tax. Nearly 34% in tax.
Between what you think of as £40k and around £42k, the marginal rate is the basic rate (20%) plus Employers NI (13.8%) plus Employees NI (12%)
i.e. around 46% - nearly half that extra money goes straight to the government so they can but some votes or print the money and set fire to it.
When you hit the 40% band, you are actually in the 40% (Higher rate) plus employees NI (2%) plus the employers NI (13.8%) or the ~56% band.
Rough percentage figures because I can't be bothered to work out if the percentages need compounding or not.