Show time: This year's Chelsea had a garden in the sky, parsnips in bloom and Cleve West's stunning winner

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Stars of the Chelsea Flower Show this year were the parsnips from designer Cleve West's allotment. His brilliant garden won Best in Show and contained the most sublime combination of plants I have ever seen at Chelsea – a complex, rich grouping, full of space and movement, with deep pools of red dianthus glowing against dark bronze fennel, and low bushes of myrtle and box anchoring greenish-white camassias and yellow alliums in a base of Cotswold brash. But the plant everybody wanted to know about was a tallish, elegant but unfamiliar umbellifer with heads of a zinging greenish-yellow.

These were the parsnips, brought from Cleve's south-London allotment, where for some seasons past he had admired the dramatic late-spring flowering of the few parsnips he hadn't dug up and eaten in winter. To me it was a new and mesmerising sight. I used to let some of my leeks grow up into seedheads (they are alliums after all) and quite regularly chicory would shoot stems of blue flowers to the sky. But who would expect such a stunning transformation from a parsnip – a metre-high explosion of intricate stems and sub-stems each topped with a flattish head of this luminous greeny-yellow?

The plants were taller than many others on the plot – not too tall, but they had enough space to hold themselves with the grace natural to all umbellifers. The fancy florists of London are going to have a job chasing after this particular plant, but I can foresee a stampede. And a shortage of parsnips for us actually to eat. The roots will all be left in the ground to flower.

The problem with many Chelsea show gardens is that there's too much happening in them. Cleve's garden had plenty of breathing space. The dimensions were those of many town gardens: a plot roughly twice as long as it was wide. In a space like that, you need to accentuate the width as much as you can and Cleve had done this by subtly dividing it into three unequal rectangles.

The central area was sunk down below the level of the beds at either end and retained inside beautifully built drystone walls, the stone laid vertically rather than horizontally. The planting here was minimal, grouped mostly round the base of the superb pillars made by sculptors Serge Bottagisio and Agnes Decoux in a dark, light-absorbing brownish-purple colour. They had an entirely modern elegance, but the form is so ancient, you can't help thinking of ruins and lost cities, with wild flowers pushing up between the fallen columns. It's like this in the classical sites of western Turkey where umbellifers such as ammi shower their seed into the smooth, hollowed grooves of fallen Greek columns.

It was actually a Roman site at Ptolemais in Libya, visited some years ago, that gave Cleve a starting point for his design. He's made a crisp, modern garden, but lurking somewhere under the surface of it is the memory of that distant, hot place and the remains of a lost civilisation. Three pillars in his garden stand in a line towards the back of the sunken centre. Another stands forward with a fallen one at its feet.

Allium cernuum gives the impression of having seeded out into the gravel from its cradle by the column. The whole garden has that comfortable and interesting air of a place that will gradually shift and change emphasis with time: the bronze fennels will ebb and flow through the mounds of bitter lemon achilleas, the New Zealand burrs (Acaena microphylla 'Copper Carpet') will advance and retreat, the dark-leaved cow parsley Anthriscus sylvestris 'Ravenswing' will seed itself about in different places, one year partnering white-flowered alliums, another year putting itself next to valerian.

The walls, ground-covering brash, and the rounded old setts used for the path that led through the two front borders and over the water to the sunken garden were all Cotswold stone. The smaller the garden, the more this kind of cohesion matters. But the path was subtly treated. Down through the borders, the setts were laid with mortar between. Over the water, they must have been anchored from beneath, because they butted up to each other with no mortar. Then beyond, where the path led into the gravelly brash of the sunken garden, they sometimes disappeared altogether, emerging from time to time as a much less distinct line through to the steps at the far end.

Loose mounds of box and myrtle anchored the planting, which was mainly of herbaceous things rather than shrubs. Four elegant, light-limbed Sophora japonica made shifting patterns of shade on the left-hand wall, rendered and painted a soft shade of ochre yellow. Five spouts poured water into a long channel which ran along two sides of the central sunken area. I wanted to sling my hammock and move in right away. This was a garden with a rich, warm soul.

Designers at Chelsea often use the device of a pavilion or summerhouse to anchor a garden in its space and each year the buildings themselves become more astounding. At the back of Luciano Giubbilei's dusty pink borders was a superb square pavilion, resting on a big slab of marble surrounded by water. The walls were made of finely woven bamboo panels, slightly S-shaped, and fixed in place by a central spindle which allowed each separate panel to move quietly with the wind. You could fix the panels together edge to edge to make an enclosed space but the delight lay in the unexpected delicacy of the angles the panels made as they changed positions. It was no surprise to learn that the building had been designed by a Japanese architect, Kengo Kuma.

There was another gorgeous building in James Wong's and David Cubeo's Malaysian garden, anchored in a lake of water lilies, with lush tropical plants lapping around the edges. This won a gold medal and no surprise. Sheets of water and lush planting provide the most natural way of cooling and filtering the air around tropical houses. This was a very sleek, modern take on the traditional courtyard and if I lived in Kuala Lumpur, provided just the kind of green cloak I'd want to wrap around me.

This was a terrific Chelsea with half the 17 show gardens winning Gold Medals. Diarmuid Gavin got his first gold, with his Irish Sky Garden, an undulating bank of clipped evergreens that was not only the biggest but was said to be the most expensive garden ever built at Chelsea. People are coy about telling you how much their show gardens cost but the figures rolling round this one ranged from £800,000 up to £2 million. Diarmuid brought me up to the eye-shaped pink pod to meet his mother, sitting serenely inside on a Lutyens bench. That was an unexpected moment and I'm as glad for her as for him that he finally got that gold.

In the Great Pavilion, too, Gold Medals went to half of the 106 nurserymen exhibiting there. Several of the medallists, like Stella Rankin of Kevock Garden Plants near Edinburgh, had never been at Chelsea before. Carol Klein chose the fabulous red-flowered meconopsis on the Kevock stand as her top Chelsea plant, a triumph for Rankin. It's not an easy plant to grow.

After a tough winter and (so we are told) the hottest, driest spring since records began, Ron Blom still managed to stage a staggering array of tulips (his son worked all through the night to arrange them), but said that in 59 years of showing at Chelsea, he had never known his tulips to bloom so early. In the run-up to the show, Avon Bulbs were using four cold stores to try and slow down the rate at which their flowers were zooming up and going over. They got a very well-deserved gold and their tall, pink- and green-flowered Nectaroscordum tripedale went straight onto the ever-lengthening list of Things I Absolutely Must Have. Chelsea is a dangerous place.