The UK government uses a complicated set of models to work out its policy on airports. One forecasts how many future passengers there will be and allocates them around different airports. Another works out the economic benefits of letting more people fly by expanding particular airports.

But any model is only as good as the numbers fed into it. WWF-UK acquired the model used by the government to work out the benefits of a third runway, and we asked an independent expert to re-run it, making a few changes – only counting benefits to UK passengers (in line with Treasury guidance), not counting taxes as a benefit (since someone has to pay them), and doubling the cost of carbon so that it falls more in line with the recommendations of the Stern Review on the Economics of Climate Change.

The result: the £5 billion benefit claimed by the government became a £5 billion loss.

We also calculated how many passengers there would be in the UK in 2030 if the government was serious about switching people to trains, promoting videoconferencing, and – most important of all – if it used a realistic price for oil.

The result: there would not be enough passengers in 2030 to justify expanding any of the UK's airports – they can cope at the size they are today.

This research not only suggests that the benefits claimed for the proposed Heathrow expansion are far from certain and may indeed be non-existent, but also that there may be no need for expansion of any UK airport. However, a full re-run of government models would be required to estimate the economic consequences of the changed assumptions.

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• Why is WWF-UK concerned about aviation growth?