Anyone with a GCSE in maths could have averted this disaster

Only Sir Richard Branson's determination to see the DfT in court triggered the reappraisal

On trains, as with planes, the preferred term to disguise a prize foul-up is "operational difficulties". Yet when this week's Transport Secretary, Patrick McLoughlin, quashed the award for the West Coast Main Line rail franchise to FirstGroup, he was refreshingly explicit.

The whole bid process, he said, must be rebooted because of "deeply regrettable and completely unacceptable mistakes by civil servants in my department". (Except, he might have added, it wasn't my department when the monumental miscalculations were made. It was – glancing back at his hapless predecessor, Justine Greening – hers.)

The taxpayer will lose tens of millions as the costs of bids are refunded to all four original candidates – roughly £1 for each British voter. Travellers on Britain's flagship railway face a further 18 months in the twilight zone while bids are tweaked and reappraised.

The incumbent, Virgin Trains, will not want to invest another Branson farthing unless and until it wins the recount.

And the frontline staff who keep the whole train set on track face a couple more years' uncertainty about whose uniform they will wear – with the renewed prospect that their future employer could be French or Dutch.

Anyone with five minutes to spare, a Maths GCSE and a £4.99 calculator from Argos could have averted the entire omnishambles by checking the civil servants' sums. Except we weren't allowed to see their flawed working-out of the risk in each bid and how to price it.

Instead, the detail of each bid remained in the DfT's Horseferry Road bunker, while Ms Greening assured the taxpaying and travelling public that the secret arithmetic was "incredibly robust".

As a bidder, Sir Richard Branson will have known more than the public and press were permitted. Yet he told the Transport Select Committee, with some exasperation: "Based on that little information we have, we believe that the rules have not been followed."

When the tycoon challenged the West Coast verdict, detractors accused him of being a bad loser.

Yet it appears that only his determination to see the DfT in court triggered the reappraisal that led to the Mr McLoughlin's confession.

Every major transport decision based on shadowy calculations must be revisited. Cheryl Gillan, MP for Chesham and Amersham, demanded an "immediate review" of the business case for the planned High Speed 2 line from London to the Midlands and beyond.

The civil servants' predictions on passenger numbers and carbon impact will prove of particular interest to both supporters and opponents of the proposed link.

Off the rails, the cost-benefit calculations for new road-building projects – or adding yet more lanes to the M25 – should also be open to scrutiny. Most pressingly, the previous Transport Secretary's rationale for ruling out a third runway at Heathrow is now open to question. It may well be that seven out of 10 UK residents exposed to aircraft noise above 55dB, and that one in four Europeans who suffer from these levels live around Britain's busiest airport.

But where are the numbers to support Ms Greening's assertion that the burden of a third runway would be intolerable?

Taxpayers may speculate about procurement blunders elsewhere in the public sector. But transport is the government department that touches more citizens than any other – making proper scrutiny essential to avoid further operational difficulties in the Horseferry Road area.