I have lost 25Kg (56lb or 4 stone) in 6 months on the Keto diet with intermittent fasting. A lot of the foods the NHS diet recommends spike blood sugar and cause insulin resistance.
Insulin resistance causes immense harm to our bodies, and the number one thing for your health is to become sensitive. This is only achieved by lowering blood sugar, which lowers insulin, which raises your sensitivity and your cells will allow their stored fat to be taken. Hench you lose weight.
It's a straightforward biological mechanism, nothing complicated and quite natural.
All you have to do is not eat about 95% of the food sold in a supermarket.