Gardens: It's the season for private plots to be opened to the public. Anna Pavord visits three creations
I have been haunting the Cambridge Botanic Garden for the last month. As haunts go, this is a good one: coffee on tap, superheated tropical glasshouses if the Fennish winds get troublesome, and an alpine house full of fabulous fritillaries, dark purple and mustard combined, which sit here like jewels in Kutchinsky's shop window.

The alpine house has a curious atmosphere, as if it were orbiting quietly out of our space and time. I think it is because the plants are so static. Each one is displayed singly in a clay pot, sunk to the rim in gravel, with various pieces of tufa rock rising gently to con the staggeringly fussy saxifrages that they are really in the Alps. I'm perfectly content to let someone else take the pain of growing them.

The alpine house was an extra. I've been at the Cambridge Botanic Garden mostly because of tulips. The national collection of species is held there, and they are planted out in a bed in the grass in front of the big glasshouse. It's been such a helter-skelter spring that flowering times have telescoped in an unusual way, and the display has been stunning.

Even the lady tulip, T clusiana, which is often shy-flowering, is making a good show this season. Its petals are narrow and tapering, and the backs of the outer ones are washed with crimson, leaving a clear white edge round the margin. The insides are white with a slight tinge of crimson at the tips. At the base is a small, rich red-purple blotch. It is named after the Flemish botanist Clusius (Charles d'Ecluse) who reported that it came from Constantinople into Europe via Florence in 1606. Clusius himself got it from a Florentine grower, Matthaeus Caccini, and it first flowered in his garden in April 1607.

The lady tulip's native home is Iran, near Shiraz, but it quickly became naturalised in southern Europe and for a while in the Twenties and Thirties was cultivated as a cut flower along the Riviera. The then foreign secretary, Austen Chamberlain, a keen rock gardener, saw it there in the Twenties. It was just emerging in spring in the garden of Henri Correvon, one of the greatest authorities on alpine plants on the Continent. "There is a minister of foreign affairs in every country," said Correvon approvingly afterwards, "but there is only one who can identify T clusiana by its leaves." I wonder if Malcolm Rifkind could do the same? It would make all the difference next Thursday, if I knew.

T clusiana var chrysantha has golden yellow flowers, the outsides of its petals stained red or purple brown. It is an easier thing to bring into flower, but hasn't the same charm as T clusiana. There are plenty of red and yellow species tulips, but few that are red and white. I'm going to be in trouble with Stanley Killingback for saying that. He likes his chrysanthas, planted in the garden that he will be opening for the National Garden Scheme tomorrow. This is the first time he's opened, and tomorrow is your only chance to see the garden.

I use the word "garden" in the widest possible sense. "Trial ground" might describe it better. Behind Mr Killingback's red-brick, semi-detached house in the north-eastern suburbs of London lies a back garden that contains tulips, tulips and then more tulips. They are planted in blocks that may contain anything from 10 to 100 bulbs all of the same kind.

Each year Mr Killingback makes copious notes on the tulips he likes and the few he doesn't. He's been doing this since the Forties, and reckons that by now he must have grown nearly 800 different types of tulip - perhaps 400,000 bulbs. And all this in a garden barely 80ft long.

There's no nonsense here about co-ordinating colours, or setting the tulip's flowers against complementary foliage, which are the things that many tulip growers have in mind when they plant. With Mr Killingback, the head count is all. Never mind the nuances, feel the numbers.

I observed that, growing tulips for so long in the same place, Mr Killingback had been lucky to avoid tulip fire, a debilitating disease that withers foliage and stunts flowers. He looked at me sternly. "Some people deserve their luck," he said.

George Adams of Pinchbeck Hall, Pinchbeck, near Spalding in Lincolnshire, is about the same age as Mr Killingback and has the same uncompromising attitude to life: you get out of it precisely what you put in. He has put a lot into his garden, which is also open tomorrow. This is a big garden, about six acres, laid out round a handsome, early-18th-century brick house, with a rather strange, tall tower added at the beginning of this century by a South African railway magnate who was nostalgic for the look-out towers of the veld.

The first thing you notice are the trees. This is partly because they are very fine - an avenue of limes, a cut-leaf beech, a copper beech - but also partly because here you are in the Fens, where trees assume a preciousness they don't have in areas further west. Like the church steeples, old trees become important landmarks. Above all, they represent shelter.

Mr Adams inherited these beauties, but has continued to plant, notably in a paddock that used to house the family pony. Here he has put a mulberry, a tree of heaven, a variegated tulip tree and a ginkgo. The Judas tree he planted on the other side of the house blew over in a gale. He's fed up about that. He went to a lot of trouble to get it, sending a meat lorry down to Notcutt's stand at the Chelsea Flower Show to collect the specimen he'd set his heart on. Meat is his business, as you would know if you lived within a 50-mile radius of Pinchbeck. He enjoys his garden.

"Well," he says, "if it isn't fun, there's no point in doing it, is there?"

Lincolnshire is a vast county and a surprising one. It must have boomed in the 18th century, for several relatively small places, such as Folkingham, have splendid and elegant assembly rooms.

Folkingham is a big surprise, set on the slope of a hill - yes, a hill - where the road opens out into a generous green. It is dominated by the Greyhound Hotel at the top, made of Georgian brick, with the grand assembly room, lit

by its Venetian window, on the right.

If you wander further on up north you will come to Holton-le-Moor, just west of the Wolds, where Philip and Vanessa Gibbons are opening their garden at Holton-le-Moor Hall tomorrow. It is bounded round the southern side by a half ha-ha, giving long views out over parkland to the Wolds beyond. This is a settled, comfortable old garden, very well treated by its owners, who have given it new hedges of hornbeam, beech, yew and holly, to break its two-and-a-half acres into separate compartments.

The house was built in 1785 and you would guess that the big kitchen garden was laid out at about the same time. The wonder here is an old espaliered apple tree - a cooker - that stretches for 73ft along a path. Some of the mossy branches go right-angled round the path corner. I've never seen a better one. Mr Gibbons thinks it may be the longest single espalier in the country. If anyone has an espaliered apple with longer branches, I'd like to know about it.

The Cambridge Botanic Garden, Bateman Street, Cambridge, is open daily, 10am-6pm, admission pounds 1.50. The other three gardens are open for one afternoon only this year. Stanley Killingback's garden at 16 Hillcrest Road, London E18, is open tomorrow, 2pm-6pm, admission pounds 1. George Adams's garden at Pinchbeck Hall, Pinchbeck, is open tomorrow, 2pm-5pm, admission pounds 1. The Gibbons's garden at Holton-le Moor Hall, Holton-le-Moor, is open tomorrow, 2pm-5.30pm, admission pounds 1.50.