Southern comfort: How a remarkable tropical garden sprung up in a corner of Camberwell

Clive Pankhurst has turned the space at the back of the house into a magnificent oasis

There are huge areas of London I know nothing about and one of them is Camberwell. So I emerged from the Peckham Rye railway station like a traveller abroad, sniffing as always for clues about how the place worked. From the magnificent maelstrom of Rye Lane (and past a fantastic great loquat hung with orange fruit in Bellenden Road) I worked my way west to Grove Park.

Houses usually get bigger as you climb uphill in London and the place I was making for turned out to be a handsome mid-19th-century brick house, set unusually far back from the road. It's now converted into five flats: Clive Pankhurst and his partner Steven have the basement and, over the past six years, 35-year-old Clive has turned the space at the back of the house into a magnificently tropical garden.

His school careers test marked him down as either a probation officer, or a jewellery designer. But he studied botany at Reading University and, as long as he can remember, has been mad about plants. "I remember, years and years ago, seeing a vast jungly-looking tetrapanax on the TV and knowing even then that, one day, I'd have to have one."

Now, a forest of tetrapanax (the rice paper plant) looms behind the pond at the back of the garden. It's a key plant for jungle-makers – huge hand-shaped leaves with the texture of grey felt and the potential to rear up to two metres or more. The bigger the better, as far as Clive is concerned. He's bravely planted the bamboo 'Shanghai 3', a type of phyllostachys which has the potential to take over the whole of Camberwell. But it's said to be the tallest of all bamboos and that's why he chose it.

For a London plot, the garden is unusually big, 40ft wide by 100ft long. Notionally, it's a communal garden, belonging to all the flats, but since Clive's parents live in the flat above him and his brother in the flat above that, he's mostly allowed to plant what he likes. There's still a bit of lawn (for his father) where a hammock is slung between an old pear and an equally old cherry tree. But the rest of the garden sings in an entirely different key.

In a corner of the terrace that opens out from Clive's basement flat are a beautifully staged set of prima donnas in pots: a Washingtonia palm, huge shining paddle leaves of banana, the even more beautiful dark leaves of the banana-leaved canna (Canna 'Musifolia') and – the greatest star of all – Schefflera macrophylla.

In pots, close to the doors opening out from the flat, Clive can keep these treasures as well fed and watered as they need. Further away, it's harder work. He feeds with pelleted chicken manure and blood, fish and bone. But the garden is overshadowed by some big trees. The soil is dry and hard to break into. Only just under the surface is a thick layer of oyster shells and rubbish. Below that is untractable London clay. And many of the plants he loves and which make the most important contribution to the look he's aiming for, are not hardy.

When it comes to plants, the bigger the better, as far as Clive is concerned (Richard Mildenhall)

In the big triangular bed by the pond at the back of the garden there's a magnificent Abyssinian banana (Ensete ventricosum 'Maurelii') with red-tinged leaves and dark red leaf stalks. How does that get through the winter, I asked? "Oh," said Clive airily, "I just give it the leek treatment." He lifts it before the nights get too cold (this banana resents temperatures dropping below 7C/45F), cuts off all the roots, shaves down the foliage and hangs the whole thing upside down in his meter cupboard until the plant has dried off. Then he wraps the plant, by now a much more manageable size, and stands it in the covered way outside the flat until it's time to start it into growth again.

This bed in the back corner of the garden is typical of the way he's worked over the past six years. At the beginning it was much smaller. Then as he collected more and more plants, he began nibbling ("softly, softly") at the lawn to make the bed bigger, hoping the rest of his family wouldn't notice. Now vast stands of plume poppy (Macleaya cordata) wave in the background, together with an even taller clump of variegated reed grass (Arundo donax 'Variegata').

There's a gorgeous clump of red-flowered Lobelia tupa close to the searingly orange flowers of the Mexican sunflower (Tithonia rotundifolia) which Clive raised from seed. "I like rich colours that stab through the planting," he explained; flowers in red, orange and yellow shine out vividly against the foliage plants in this garden. The cactus dahlia 'Chat Noir' looked particularly good in the triangle bed, alongside the chalky orange spikes of a red-hot poker (Kniphofia rooperi). A paulownia, cut down to the ground each year, shoots up with leaves as big as tablecloths, easily overtopping the seed-raised castor oil plants and the papyrus.

There's a surprise in this garden that you aren't aware of at the beginning. On the right, a flight of steps breaks into the brick boundary and leads you up into a space almost as big as the first. Once it must have belonged to the neighbouring houses but by the time the Pankhurst family arrived in Grove Park, it was a fenced-off piece of wilderness. A few years ago, they were able to buy it and – after five skip-loads of rubbish had been carted away – Clive started to plant his tropical vision: a jungle, with a patch in the middle for growing food. On the boundary, he's already established the most terrifying plant I've ever seen, Kalopanax septemlobus with thorns as sharp as a kukri. Be afraid, residents of Grove Park. Be very afraid.

The garden at 24 Grove Park, London SE5 is open tomorrow (2-5.30pm), admission £3, children free. Check it out at Clive's blog, alternative-planting.blogspot.com