If ever there was an English national literary treasure, he must be Edward Lear. In polls, including a recent one for National Poetry Day, The Owl and the Pussycat is often voted our favourite poem. Anyone who has ever doodled a limerick, of any tone or topic, pays homage to his genius. As well as timeless nonsense such as The Jumblies, there’s also his art – brilliantly studied paintings of exotic creatures in far-off lands; luminous desertscapes; antic sketches of men with birds in their beards – work that puts him in a class of his own as an important Victorian artist.

Edward Lear is one of those English one-offs who are treasured because they seem to suggest that there are no more important things to do than paint or write, and who embody a benign, provisional and above all amateur spirit. Lear himself, slyly complicit, summarised his place in the English cultural landscape with a teasing, encrypted self-description:

How pleasant to know Mr Lear!
Who has written such volumes of stuff!
Some think him ill-tempered and queer,
But a few think him pleasant enough.

He was born in London in 1812, the same year as Charles Dickens, one of at least 17, or was it 19 (his mother lost count; there were infant deaths)? Young Edward was both swept up in, and set apart from, this brood. With good reason, he always felt different. By the age of five, he was not only a boy among many sisters, but also diagnosed as epileptic, a lifelong terror he shared with Lewis Carroll. Epilepsy would be one of the secrets that made him solitary, while his atrocious eyesight “formed everything into a horror”. Lear’s nonconformist parents hardly compensated for these childhood traumas: both were largely absent. His City broker father was remote; his “shadowy” mother rejected him.

Jenny Uglow declares at the outset that she wants to “follow his life straightforwardly”. In this, she’s echoing the discreet and magisterial example of Vivien Noakes who pioneered this elusive subject in 1968 in Edward Lear: The Life of a Wanderer. But Uglow goes much further than Noakes. This, quite rightly, is the half-life of a gay man in a society that had neither language nor tolerance for homosexuality. By chapter two, on top of all his other troubles, young Edward is grappling with some mysterious abuse, “the greatest evil done to me in my life”. What, exactly, this was remains unclear, though Lear recorded the date of the “greatest evil” every year in his diary. Uglow, whose focus on Lear and his confused sexuality is unflinching, is too good a biographer to indulge in reckless speculation here. Clearly, for “pleasant” Mr Lear, nothing would ever again be “straightforward”, especially once he and his beloved sister Ann began to escape into a parallel universe of exquisite botanical drawing. Nonsense verse soon followed. From boyhood, Lear was “three parts crazy”, but “wholly affectionate.” He would only get more like himself.

There were few intrusions on his adolescent solitude, apart from birds, especially parrots, his favourites. Some early zoological work inspired his vocation as an artist. Eventually, he would rival Audubon. Parrots also brought him a patron, Edward Smith-Stanley, 13th Earl of Derby, whose teeming family exposed Lear to a new audience for his gifts as an entertainer. As an artist, Lear was supposed to remain below stairs with the servants, but Stanley liked to have his protege upstairs to amuse his guests. Where Carroll had Alice and the Liddell family, Lear had the Knowsley nursery, where the Stanley children, their friends and nursemaids, kept riotous company. Unlike Carroll, he did not sentimentalise little girls, betraying no hint of the paedophile. Rather, Lear loved the mayhem of childhood to which nonsense was the only answer. Nonsense was infantile, rude, eccentric and grumpy, as children are. Nonsense could celebrate surreal violence and ghoulish accidents. As a roving landscape painter, Lear could be exquisite. Through his crazy wordplay, he could express his inner torment as a homosexual single man in Victorian England.

Abroad, in Rome or Corfu, he could be “as happy as a hedgehog” and was free to fall in love with other artists. At home, he had to present himself, half ironically, as a man in need of a wife: “I anticipate the chance of a Mrs Lear”, he wrote, “in 40 years hence.”

Unlike some gay Victorians, who went native overseas, it was Lear’s respectable hope that he was “always an Englishman” abroad. “Mr Lear” was certainly a weird bird. As he grew older, this myopic court jester, and nomadic artist, unable to reconcile his sexual with his social self, morphed into his mature, eccentric persona.

This was the closet homosexual who, in the summer of 1846, came to teach drawing to Queen Victoria. “How did you get all these beautiful things?” he exclaimed, on first seeing the famous royal collection. “I inherited them, Mr Lear,” replied the Queen.

It’s at this point that Jenny Uglow diverges most completely from the narrative line hewn by Vivien Noakes. Uglow’s interest in Lear’s court life is distinctly finite. And yet Windsor did do something for Lear, which was give an awkward, gay man renewed self-confidence. Thus, 1846 also saw the publication of A Book of Nonsense (now an exceedingly rare book). Uglow is good on Lear’s nonsense, attributing just the right amount of consequence to its surreal caprice:

There was an Old Person of Rhodes,
Who strongly objected to toads;
He paid several cousins,
To catch them by dozens,
That futile Old Person of Rhodes.

On his travels again – now to the Holy Land – Lear fell in love with a younger man, Frank Lushington, who would eventually compound Lear’s inner torment. For a while, the senior partner found temporary solace among the pre-Raphaelite brotherhood to whom he looked up as a child among grown-ups, addressing Holman Hunt as “dear Daddy”.

Now in his 40s, Lear had become a considerable figure in the mid-Victorian arts world, making friends with Tennyson and especially his wife, Emily, to whom he confessed feeling “jarry and out of tune”.

Uglow shows that the life of the Victorian gay man, even in progressive circles, was excruciating. The sexual appetite, wrote one, was “a beast to be suppressed, trampled by the help of surgeons and their cautery of sexual organs”.

Only abroad could Lear and Lushington enjoy a semblance of marriage – as Uglow puts it – “without the sex”. But then, how “queer” was Mr Lear? When he and his manservant Giorgio visited Mount Athos, Lear fled screaming from the Holy Mountain and its “mournful, minced fish and marmalade masticating Monx [sic]”.

In middle age, Lear’s wordplay had become quasi-Joycean, writes Uglow, “alive, protean, ever evolving, and finding new endings, like new limbs”. This is the Lear beloved of Auden and Eliot. He was, says Uglow, “an eerie, queery, sometimes weary, sometimes cheery Edward Lear”.

When “cheery”, he enjoyed moments that were “splendidophoropherostiphongious”, but there was always a terrible sadness, too, that only nonsense could assuage.

In 1861, Lear published a new Book of Nonsense, a huge success that would establish him as a classic. Four years later, Lewis Carroll published Alice in Wonderland, a very different kettle of fish, steeped in logic and literary allusion. These two Victorian giants never met, and Lear read Alice “without comment”.

Lear’s world, unlike Dodgson’s Oxford idyll, was provisional, nomadic and fraught. Lushington got married and Lear tortured himself with matrimonial fantasies. He would be “forever roaming with a hungry heart”.

Finally, the gaiety and sadness of Lear’s life expressed itself in his four greatest poems: The Owl and the Pussycat, The Dong With a Luminous Nose, Some Incidents in the Life of My Uncle Arly and The Jumblies, warbling their “moony song”. He might recognise that he had gone “to sea in a sieve”, but he admonished his diary that “the morbids are not allowed”. This extraordinary Englishman died in self-imposed isolation in San Remo aged 75. Jenny Uglow has written a great life about an artist with half a life, a biography that might break your heart.

• Mr Lear: A Life of Art and Nonsense by Jenny Uglow is published by Faber (£25). To order a copy for £21.25 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99