Britain has now posted three consecutive quarters of declining gross domestic product – the most recent figures show the economy has shrunk by 0.5%. With the latest set of GDP figures due to be released later this week, the nation remains sunk in the longest recession since the second world war.

But GDP is also coming under a different sort of scrutiny in these days of economic woe. GDP measures all legal transactions in the financial economy – no more and no less. And yet, since its inception in the 1930s, it has become the single most important policy tool for governments, financial institutions and corporations. Governments and many people believe that only this one miraculous figure can really show whether things are getting better or getting worse.

But GDP is a partial and misleading measure of national wealth and wellbeing. The problem is that it does not measure key goods in our economy, those unpriced but priceless services carried out by domestic workers and by nature – for example, the coastal defence of coral reefs, the pollution-filtering of wetlands, the nutrient recycling done by the soil and the unpaid work we do in our homes.

And yet GDP does include bad elements such as pollution, crime, cigarettes and their related health costs and environmental disasters, which boost GDP and so generate economic growth.

These omissions and inclusions generate alarming anomalies. Here are two: we are better economic agents if we eat out at expensive restaurants rather than cooking food we've grown at home; cleaning up the 2010 BP oil spill in the Gulf of Mexico was worth more economically – in GDP terms – than the carbon absorption provided by the Amazon rainforest.

Under current GDP measures, countries that cut down forests for timber exports, dynamite their reefs for fish, pollute and degrade their soil for intensive agriculture and allow farms and factories to contaminate their waterways get rich.

The services provided by nature and households are not included in GDP because we consider their work to be free. But these services are not free – and we are beginning to pay their hidden costs in environmental destruction and climate change.

Conceived in Washington DC during the Depression, the GNP (as it was then) was flawed from the outset. Even its creator, Simon Kuznets, argued that it was a partial measure of national wealth, as did economist John Maynard Keynes, who oversaw the construction of the first British national accounts during the second world war.

Both Keynes and Kuznets considered these figures to be temporary measures, for use only in emergencies such as wars and depressions. But they quickly became enshrined in public life, and after the second world war they were imposed on almost every nation on earth.

The first politician to rail publicly against the GDP was Senator Robert Kennedy in March 1968: "Too much and for too long, we seemed to have surrendered personal excellence and community values in the mere accumulation of material things. Our Gross National Product … counts air pollution and cigarette advertising, and ambulances to clear our highways of carnage." For Kennedy, GDP measured "everything, in short, except that which makes life worthwhile".

It took 40 years for Kennedy's words to reach Washington DC: in March 2008 a US Senate committee discussed GDP's failure to measure environmental damage, poverty, income inequality, health and the quality of life. Two years later, Obama's healthcare bill allowed $70m over eight years to develop a new system of US national indicators. Economists from the group the State of the USA are now working to generate 10 to 15 key measures from a set of some 300 indicators, including health, education, crime and justice, art and culture, the environment, and the economy. These new, more comprehensive measures are designed to guide US policy in an era of environmental destruction and economic downturn.

GDP has been similarly challenged and deconstructed in Europe. In 2009, the then French president Nicolas Sarkozy recruited a team of economists "to tear the GDP apart as they saw fit". They too found that GDP should be replaced and that other indicators should be introduced to monitor social and environmental, as well as economic, change.

The UN is working to value ecosystem services – or natural capital – and this year adopted a new international standard to give natural capital equal status to GDP. Speaking at the UN's conference Rio+20, Nick Clegg said the UK was committed to including natural capital in its national accounts by 2020.

One notable exception to the reign of GDP across the globe is Bhutan, which for the last four decades has used "gross national happiness" as the important measure, instead of GDP. With its long experience of alternative measures, Bhutan is now instrumental in current debates about national wealth and wellbeing.

These initiatives to tear GDP apart are still in progress, but they make it clear that GDP's 80-year reign as the unchallenged measure of national wealth is at an end.