When Charles Dickens picked up his quill in 1859 to write the words, "It was the best of times, it was the worst of times," at the top of a clean sheet of paper, he was setting down some of the most enduring opening lines in world literature. The novelist's striking phrase helped to set the scene for his celebrated story of love amid the turmoil of the French Revolution, but the famous passage with which he began A Tale of Two Cities might not endure for much longer without urgent intervention.

This weekend the Victoria and Albert Museum is launching a campaign to raise funds to conserve the original manuscripts of three of Dickens's best-loved works, including A Tale of Two Cities. Rescued from the novelist's home by his close friend John Forster, the manuscripts came to the V&A in 1876 when Forster, a literary agent, bequeathed his library to the fledgling museum.

The V&A now hopes to restore the priceless originals – which are still legible although blotched and underscored – in time for international celebrations of the bicentenary of Dickens's birth in 2012. "At the moment we can't display these manuscripts safely because they are so damaged and so fragile," said John Meriton, deputy keeper of word and image at the V&A. "They were last conserved in the 1960s, when they were rebound and placed in what are called 'guard books'. But the backing paper used, unfortunately, was very acidic, causing a lot of stress to the original manuscript leaves."

Some parts of the manuscripts are also impossible to read because the leaves were pasted down, making the left hand or verso pages inaccessible.

If the museum – which, like other national heritage institutions, is now facing severe budget cuts – can raise £25,000, curators say it will be able to protect the full manuscript of A Tale of Two Cities, the story of the love between Lucie Manette and the aristocrat Charles Darnay, as well as the original manuscript of the equally loved David Copperfield, published in 1850.

The third manuscript is Dickens's perplexing, unfinished last novel, The Mystery of Edwin Drood. If this manuscript is restored and conserved, museum visitors and Dickens scholars will be able to study the author's own notes and textual alterations and even perhaps deduce their own solution to one of the most intriguing unsolved cases in literary history.

"You can see the corrections Dickens has made to each section of the stories," said Meriton. "And these are the pages that he would have handed into the printers for typesetting, before receiving the galley proofs for correction in return. We have some of those proofs too, and so it will be possible for visitors to trace the editing process that went on."

Written in "iron gall" ink on low-grade blue writing paper, purchased by the author from WH Smith, the manuscripts were never "wonderful quality", according to Meriton. But they remain a crucial part of Britain's cultural heritage.

"It is an immense privilege to have them in the collection and just to see Dickens's rather crabby handwriting is a real thrill for me every time," he said. The museum has already raised more than half of the money required to conserve the manuscripts. If it can raise a further £25,000, it hopes to be able to remount each leaf on non-acidic backing paper, after gently steaming out the worst creases. The restorers will also need to release the old bindings and mountings, and to clean the pages in an expensive humidifying process. "We have managed to conserve our other Dickens manuscripts, some of which were in a more stable condition, but the money just ran out," said Meriton.

The extra £25,000 will pay for the work of a specialist conservator, as well for new alkaline paper, protective boxes, and for units ensuring safe levels of humidity around the manuscripts. The biographer and author Peter Ackroyd is backing the V&A's push to preserve these manuscripts and said this weekend that they "are an invaluable treasure for the nation and its culture".

The museum's directors believe that, as well as showing the different quills, nibs and inks the author used as he travelled around Britain, the repaired manuscripts could offer an unparalleled opportunity to study the author's process of planning, writing and correcting.

If the work is completed, the books will be available to view by appointment in the National Art Library, the V&A's major public reference library. They will also form part of a Dickens display at the National Art Library in 2012 as an element of Dickens 2012, an international festival of celebrations.

Meriton suspects that without the actions of Dickens's friend Forster, who edited newspapers as well as penning a two-volume Life of Charles Dickens in 1872 and 1874, the manuscripts would have been thrown in the wastepaper bin or burned on the fire. "I don't think Dickens would have kept them at all if it had been up to him," he said. "He was not that interested. It was Forster who saw their value and who, I think, realised they would help with a future biography."

A Tale of Two Cities, which remains one of the most popular novels ever written, was first published in weekly instalments rather than monthly, unlike most of Dickens' novels. The first episode ran in the first issue of Dickens's literary periodical, All the Year Round, on 30 April 1859 and the dramatic conclusion ran 31 weeks later, on 25 November.

Just like the self-sacrificing Sydney Carton, who is giving the closing lines of the novel as he steps up to the guillotine in place of another man, donors to the V&A conservation cause may perhaps feel: "It is a far, far better thing that I do, than I have ever done."