The reason behind Tim Spector not advocating calorie counting is that it is based on science that we now know is flawed. The way the calorific content of food is measured is to dry it, then burn it. Which is great for working out the amount of energy you would get from the food if you were using it to heat your house, but the body doesn't work that way. Some food with a high calorie content is passed through with almost none of the calories extracted. Other foods, typically those high in fibre, take a lot longer for the digestive system to extract the calories, and for others we use significant energy breaking them down to digest.
So while eating fewer calories is generally good if you are trying to lose weight, it may not help too much if you were eating mostly high-calorie, but high-fibre foods and replace those with lower-calorie and lower-fibre.