In the bowels of BFI Southbank, the National Film Theatre as was, I am sitting in a viewing cubicle in a whole corridor-full of viewing cubicles, wading through a pile of video cassettes and DVDs. Some are of appalling quality, the picture flaring up at the edges and with almost inaudible sound, but most are exactly as they would have appeared when first broadcast on the nation's black-and-white television sets in the Fifties and Sixties. Welcome to this year's harvest of rediscovered TV in the British Film Institute's Missing Believed Wiped initiative, which, introduced by expert speakers, will receive a public showcasing on the South Bank this Sunday, 14 December.

"Missing Believed Wiped has been running for 15 years now," says the BFI's TV programmer Dick Fiddy. "It began with an earlier BFI initiative called 'Missing Believed Lost', which helped to find British films from the silent era and the early talkies. I thought that we should extend this to television."

And the first two decades of British television are in dire need of preservation for, as Fiddy explains: "Either it went out live and wasn't recorded in the first place, or the video tapes it was shot on were simply re-used. This capacity for being recycled was ironically the great selling point to broadcasters at the time," says Fiddy.

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Other programmes disappeared into skips, warehouses and private homes. "I knew that a lot of television had survived in odd places," says Fiddy. "It had been in the wrong archives, or in the hands of private collectors, or in the hands of people who used to work in television and who had taken copies home with them, never realising the rarity of what they had. Now, year after year, we get enough material coming out of the woodwork to hold an annual review."

This year's Missing Believed Wiped review contains tapes presented to the BFI by TV presenter David Hamilton, aka David "Diddy" Hamilton", and from the late Bob Monkhouse. Hamilton's offering was a recording of the valedictory final night's broadcast by ABC, the ITV regional franchise holder from 1956 to 1968 that was not only responsible for beauty pageants from Prestatyn and "the first live pictures from the Isle of Man", but also for such television gold as The Avengers and Armchair Theatre.

There's a fascinating glimpse on Hamilton's ABC retrospective of an Emmy-winning Armchair Theatre production called Call Me Daddy, with Donald Pleasence and Judy Cornwell. Most Armchair Theatres have however been lost.

"Probably the most fabled missing drama is Philip Saville's Madhouse on Castle Street, which starred Bob Dylan in 1963 – very early in his career," says Dick Fiddy. Music shows are also particularly vulnerable, with whole swathes of Juke Box Juries, Thank Your Lucky Stars and Top of the Pops from the Sixties seemingly consigned to oblivion. Fortunately, the BFI has found that a lot of the programmes have survived abroad, where their origins aren't initially recognised. "Some performances were sold internationally to other shows and we've managed to get those back," says Fiddy. "Twenty-five or 30 years down the line a German or a Swedish broadcaster might realise that a three-minute pop song they thought was produced earlier was actually from Top of the Pops. There are researchers who can look at a performance and know instantly that it's Top of the Pops or Ready Steady Go, or Oh Boy!."

The estate of Bob Monkhouse has provided two of the programmes in this year's Missing Believed Wiped review: The Flipside, a BBC Thirty-Minute Theatre from 1966, with Monkhouse in a rare straight role and an American accent, and a risqué episode from his 1957 sitcom My Pal Bob, in which Monkhouse and writing partner Denis Goodwin tried to emulate the style of the long-running Lucille Ball hit I Love Lucy on British TV.

"Monkhouse was a supporter of Missing Believed Wiped and even introduced the event one year," says Fiddy. "During conversations afterwards he intimated that he had some missing TV within his collection – missing Sunday Nights at the London Palladium, and this play The Flipside, which he said he'd give to us. Unfortunately, he died before handing them over. Obviously, there's a hiatus when somebody passes on – you can't go knocking on the widow's door the next day. But you can't leave it too long in case they start throwing stuff away. I once tried to get the BFI to come up with a donor card for people with huge collections..."

The family of the late Alistair Sim also approached the BFI, with a 15-minute gem dating back to 1952 in which Sim, sitting increasingly uncomfortably in a wing-backed leather armchair, delivers a monologue to camera about the difficulties of delivering a monologue to camera. Unlike the rather cheesy Monkhouse sitcom, this is genuinely funny stuff, decades before Alan Bennett's TV monologues or Ronnie Corbett asked us whether we were sitting comfortably. And it wittily goes to the heart of the relationship between TV performer and the viewers "staring at me like a multitude of expectant ghosts".

Also eye-catching is a rediscovered series called Chelsea at Eight, found by an archivist among a collection of travelogues. This 1950s Granada precursor to Friday Night with Jonathan Ross was filmed in the then bohemian London neighbourhood of Chelsea, in which anybody passing through was dragged into a makeshift studio. Among the finds are Billie Holiday singing "Strange Fruit" and John Osborne reading from one of his plays.

The same archivist also discovered a pile of "admags" – a part of television history thought to have become extinct. "Advertising magazines, or 'admags', were outlawed in the early Sixties," explains the BFI's Dick Fiddy. "They were a 15-minute semi-soap opera in which stars – Katie Boyle was omnipresent – soft-sell goods. They were believed to be rather too insidious. They were well done and popular and very few existed until recently."

Also unearthed were a whole collection – from someone who used to make them – of BBC trailers from the 1960s. "That sort of nitty gritty of television – the continuity shorts, the flotsam and jetsam between the programmes – are the sort of thing that don't usually survive," says Fiddy. "It gives you a much better idea of what Sixties television actually looked like."

But this year's Missing Believed Wiped is going beyond the usual remit of showing freshly rediscovered television – it is also getting into the business of restoration. More particularly it is showcasing a new process whereby old TV programmes filmed in colour but shown in black and white, like some early episodes of Doctor Who, Dad's Army and Top of the Pops, can be now be shown in colour.

"The black-and-white tele-recordings actually carry colour information in the form of dots and BBC boffins have worked out a way of reversing the process," explains Fiddy. "This is the first public demonstration." Actually, the BFI is being pre-empted by BBC2, which on Saturday night will be screening a remastered episode of Dad's Army that hasn't been seen in colour for almost 40 years. "This initiative could become commercially important, if you look at some of the early Doctor Whos that only exist in black and white. It could also become culturally important if you look at something like Nigel Kneale's 1968 drama The Year of the Sex Olympics, which was made in glorious colour and whose colourful sets and costumes are part of the plot.

"It's not a gimmick. This is not colourisation. Colourisation was always naff because if something was shot in black-and-white, it was lit for black-and-white, it was costumed for black-and-white. If something was made for colour and you are just putting the colour back then you're retrieving it.

Meanwhile, the BFI's annual event is encouraging more and more hitherto presumed lost television footage back into the open. "We've had to cull heavily all the available new material," says Fiddy, who adds that the BFI also now runs impromptu events during the rest of the year. "We had a hugely successful screening of something called The Complete and Utter History of Britain, which was Palin and Jones's last sketch show before Python, and which was very Pythonesque – three episodes now survive of that. We showed that to a packed house at NFT1.

"Our audiences are a mix of enthusiastic amateurs, professionals from the business, archivists and collectors – it's almost like a convention."

But private collectors can be a paranoid bunch, he says, who sometimes need "handling with kid gloves". Fiddy is as anxious to reassure them. "At one time, people were reluctant to come forward because they thought they'd be prosecuted, for whatever reason. But the BBC and ITV over the past 15 or 20 years have been much more enlightened about that – they are just anxious to get the stuff back."

'Dad's Army in Colour' is on BBC2 on 13 December at 8.25pm; Missing Believed Wiped is at the BFI Southbank ( www.bfi.org.uk ) on 14 December