For some it's John Noakes crying over the death of his beloved Shep, for other's it's Yvette Fielding's disastrous cooking demonstrations and for those who never managed to get their hands on the show's sought after badges or whose competition entries always seemed to get lost in the post, it's a memory of dashed childhood dreams.

Since it first aired back on October 16, 1958, Blue Peter has remained a constant on the BBC and, despite occasional tweaking, the formula has remained largely unchanged. Now, having secured unprecedented access to the Blue Peter archive, the National Media Museum in Bradford is putting the finishing touches to an exhibition on everything you ever wanted to know about bring and buy sales, Christmas appeals and the enduring popularity of the show which started as one 15-minute weekly broadcast 50 years ago.

"There have been so many iconic moments," says Claire Thomas, assistant curator of television at the museum.

"You only have to mention its name and people instantly remember the trio of presenters who were on the sofa when they were growing up.

"Over the years, the combination of the domestic, the unexpected, the adventurous and the extraordinary has proved a compelling formula. Our plan is to have a television set from each decade showing classic clips from the show, from the earliest surviving footage which dates back from 1963 right up to the present day."

It's impossible to imagine a history of Blue Peter which doesn't mention Lulu the elephant, who famously defecated on the studio floor, before treading on John Noakes's foot and attempting to make a quick exit or the Girl Guide campfire which got out of hand in 1970, leaving the assembled children and a half a dozen Brown Owls choking on the thick black smoke. However, while the exhibition will inevitably remind visitors of Noakes's attack of vertigo as he helped clean Nelson's Column or the competition to improve Peter Duncan's dress sense which left him sporting an unflattering green and white harlequin suit, it also promises to explore behind the scenes of the show.

"The idea is to dig a little deeper," says Claire. "We want to look at how the elements of the Blue Peter formula were constructed to complement the programme's values. The badges were introduced to encourage interaction between the viewers and the presenters, the summer expeditions were designed to take all children round the world and the pets and the garden allowed viewers to share responsibilities which they might not experience at home."

Today, it's easy to view those early programmes and the presenters who became household names using sticky backed plastic as evidence of halcyon days when children were content to spend their time collecting stamps for Third World Appeals. However, amid the cookery demonstrations and lighting of the advent wreath, Blue Peter has had more than its fair share of groundbreaking moments.

In 1971, the footage of Valerie Singleton accompanying Princess Anne on a trip to Kenya with Save the Children showed a previously unseen side to the Royals and brought the problems of Africa into people's homes long before Sir Bob Geldof came on the scene.

The following year, it broadcast the first colour images on British television of the onboard fire which sank the RMS Queen Elizabeth in a Hong Kong harbour – and, from the vandalism of the Blue Peter garden in 1983 to the on-air apology in 1998 after presenter Richard Bacon admitted to taking cocaine, there has rarely been a quiet 12 months.

However, the last two years have arguably been the most difficult period in the show's history. In 2006, it emerged that a phone competition supporting a Unicef appeal was rigged. The caller was not a lucky viewer, but a child who happened to be visiting the studios. The show was fined £50,000 by Ofcom, but worse was to come. In September last year, just a month after the Conservative Party accused Blue Peter of political bias for allowing presenter Konnie Huq to take part in a press conference about the benefits of cycling along with the then Mayor of London Ken Livingstone, the Cookie-gate controversy broke.

It emerged that in an online vote to name the new Blue Peter kitten, the majority of viewers had opted for Cookie, but worried the choice could somehow be seen as fuelling childhood obesity, the show decided on the less offensive Socks.

Some were quick to write the programme's obituary, but after 50 years of highs and lows, if there's one show has proved it can ride a storm it is Blue Peter.

Here's One We Made Earlier... 50 Years of Blue Peter opens at the National Media Museum in Bradford on October 18.