All British political parties now support the idea. See the ONS consultation on Measuring National Wellbeing. So too does the club of rich nations (the OECD) and many individual foreign governments. Such measurements are not new. Happiness has been measured regularly in the United States since the 1950s, and in the European Union's Eurobarometer it began around 1970. What is new is that these measurements are being made on larger samples and given official status.
That is all to the good because if you measure the wrong thing you do the wrong thing. Governments began measuring the GDP in order to manage unemployment, but they allowed it to become the totem of national success. This simply confirmed the materialistic, consumerist values of the wider society. It is great that this now changing.
The aim of measurement is to see who is languishing and, having found the causes, to adopt policies to improve things. To find this out people are asked questions about how happy they are, how satisfied with their life and its different dimensions, and so on. These measurements get high response rates. But do they mean anything? The answers are, as intended, totally subjective. But they are well-correlated with all kinds of objective measurements.
First they are correlated with brain activity in the relevant areas where positive and negative feelings are experienced. Second, they are correlated with behaviour - people who say they are unhappy at work tend to leave their jobs. Third, what people say is correlated well with obvious causes of happiness and misery, like unemployment. And fourth, what a person says about his happiness is echoed by what his friend say about him - if we could not perceive each other's subjective feelings, human society would be impossible.