The statistics, seen by Money Mail, highlight how rules – introduced in March to help pensioners get a better payout – are failing.

They show that in the first four months after the introduction of the new code, tens of thousands of retirees missed out on the best pension.

In fact, despite promises that the reforms would lead to far more people seeking better deals, the figures reveal they had barely any impact. And only a tiny proportion of sick savers get enhanced deals from their pension providers.

Alan Higham, founder and director of advisers Retirement Angels, said: “Insurers make billions from loyal customers who stay with them and don’t shop around – they won’t want to lose that overnight.

“The new rules are nothing more than a very superficial message from insurance firms to avoid formal regulations being imposed on them.

“In reality, these insurers are in a privileged position and are exploiting the loyalty of their customers, who will stick with them.

“Most people switch to panic mode when they retire and take the first deal they can get – and this is enormously profitable for that firm.”

When someone retires, they will be sent a quote from their insurer showing how much it will offer them as an annual income, known as an annuity. Retirees, though, should always shop around. This is because what insurers quote is generally for a very standard type of customer.

They may not give bigger incomes to the sick or to smokers, who can get 40 % cent more because they have shorter life expectancy. Married savers often do not realise they can get a type of pension which continues paying out to their partner after they die.

And even on standard deals, rates can differ vastly between insurers, with the better firms offering up to 20% more.

In 2012, 419,587 workers took an annuity. Of these, 52% kept a whopping £5.5bn with their existing insurer. The fear has long been that many of these will have failed to realise it is possible to qualify for a better deal.

In March this year, trade body the Association of British Insurers introduced a new code of conduct that is supposed to encourage more retirees to shop around for the best pension. It was brought in only after a fierce debate among members – many of whom had resisted change for years.

Key parts of the new rules ban insurers from sending out jargon-filled letters to retiring customers. They must also promise not to include unrequested quotes without sticking to tough conditions, or send out application forms without being asked.

And they must make it clear to their customers that they may get a better income by shopping around.

Despite this, the leaked figures show that from April to July, 52 % of retiring workers still stuck with their existing insurer, handing over £1.3bn. Of the 43,255 who took professional advice or shopped around, 19,341 took an enhanced payout because they were sick. Yet of the 47,251 who stuck with their insurer, just 2,969 got an enhanced deal.

While it is possible a greater proportion of sick retirees take advice, it is still likely to mean thousands, even as many as 18,000, have lost out on a bigger pension. That means someone signs up to an unsuitable pension every seven minutes, each day.