Rachel Whiteread is famous for her grand sculptures. But Rachel Whiteread's smaller works – from her doll's house furniture to a cast of Peter Sellers's nose – delight Adrian Searle.

 Talismanic … objects collected by Rachel Whiteread

Rachel Whiteread's art is almost entirely concerned with the places where we live, and the places where we might also die. In the end, it all comes down to the empty room, the table and chair, the space under the stairs, the mattress and the bath, the light switch, keyhole and door knob, a life packed away in a cardboard box on a shelf. It's an art of understatement and reserve: she knows how much and how little to say, leaving us space to think and interpret. Simple things fixate her in the same way that they might loom in the imagination of a child.

The show of Whiteread's drawings at Tate Britain is a kind of reconstruction of her career to date, starting from the late 1980s (a further show of drawings, and a new sculpture, are also at London's Gagosian). The Tate show reveals her preoccupations in a way that is direct, intimate and readable. A few sculptures – including her 1988 felt-covered Closet, and a 1995 model for her Holocaust memorial in Vienna, finally erected in 2000 after a long political wrangle – punctuate the exhibition, but the real fascination lies in her drawings and collages.

Whiteread's sculptures often present a kind of monumental blankness that resists us, while her drawings are more revealing. With their delicate fields of paint, their freehand lines in ink and pencil, and their layers of typewriter correction fluid, these small-scale works have an approachability we don't often feel in the presence of her sculptures. They might capture the brooding presence of a closed door, or a seemingly endless flight of stairs, which appears more exhausting to contemplate than to actually climb. Taking an old furniture advertisement, with its half-tone pictures of heavily upholstered settees and easy chairs ("3-piece suite £21"), Whiteread obscures the entire page with dull grey paint, leaving only a single ugly chair, sitting in dismal isolation. The image looks like a memory from a 1950s childhood, the gigantic, lumbering chair a stand-in for adult presence.

There are no people in Whiteread's art, but their presence is everywhere: the spills of varnish that bleed beyond the contours of a drawing of a table; the way tracing paper puckers around a layer of yellow acrylic that describes a bed (ending up looking like a rumpled sheet); the spatters that surround a drawing of a bath. All these hint at human occupation and bodily traces. The plainness of her outline drawings of rooms, windows and house frontages invite the viewer to project occupants – and domestic scenes – on to them.

Only one group of drawings makes direct reference to the human form. These are a number of outlines of child-like heads, seen mostly from above; they were meant as studies for a font for St Paul's Cathedral, which never came to fruition. One inspiration for them was a 15th-century diagram of a head by Piero della Francesca, an Italian artist and mathematician.

Ghosts among the rubble

Whiteread's pencil and correction fluid outlines wobble across the paper, their apparent tentativeness itself a kind of liveliness. The works have a frankness, a lack of affectation or mannerism, which to my mind makes them all the more approachable and direct. They have a sort of winning honesty: they are more about ideas than demonstrations of graphic skill. One group describes a parquet floor, with a herringbone pattern. In one white-on-black drawing, the wood blocks click-clack across the paper, the pattern undulating like an ocean swell, just as it might to the eyes of a child. The whole thing has a seasick quality. Stray blobs punctuate the wonky, out-of-kilter pattern. Ruskin wrote somewhere of his own boyhood fascination with the whorls on floorboards and the patterns on the carpet, as he played on the floor with a bunch of old keys for a toy. Some of Whiteread's drawings capture just such a state of reverie, provoking a similar daydream-state in the viewer.

It is now more 20 years since Whiteread made Ghost, her seminal plastercast of the interior space of a Victorian front room. When it was finally shown, the sculpture looked inevitable: so simple, so direct, so unfussy, never mind the complications of making, removing and assembling the sections of the cast. Ghost looked both familiar and uncanny, making the kind of room many of us in Britain have grown up in, and continue to live in, appear suddenly alien and strange. It gives us a jolt.

This same spirit is in Whiteread's overpainted photographs of a terrace in Hoxton Square, and a decrepit row of houses in Mile End, east London, one of which Whiteread eventually used as the mould for House, the 1993 work that made her international reputation. In the photographs, we see walls, doors and windows effaced by thick, pasty Tippex, creating ghostly presences amid the builder's rubble, the scaffolding and the crumbling brickwork; the Tippex drowns out the London grime, the signs of occupation and dereliction.

Further on in the show, there are postcards of cloisters and medieval church interiors, the images punctured by numerous round holes, letting in air and light, and dizzying the architecture with a colander of holes. Other postcards are edited with paint, correction fluid and scribbled ink, leaving mysterious, ambiguous half-images. These reworked postcards, we are told, are the sorts of thing the artist works at on her travels, sitting in hotel rooms.

Is that a human intestine?

The show concludes with a selection of objects collected by the artist, providing a further clue to her thinking. There are little groups of doll's house furniture, a number of bird houses (looking like weatherbeaten beach huts), and the glass cast of what seems to be a human intestine. Old tin jelly moulds and casts of the human brain sit alongside bits of fossil, a chunk of the Berlin wall and – bizarrely – a cast of the comedian Peter Sellers's nose. What the artist's eye alights on, and delights in, is always fascinating. These talismanic objects feed Whiteread's imagination in unaccountable ways. Just having them around might provoke a thought, an idea, a new beginning.

Kafka, talking about the process of writing, wrote that there was no reason to leave one's desk: that if you sit there long enough, the world "will writhe before you". So it is with Whiteread's art. Work often springs from a kind of creative emptiness, and frequently involves a lot of footling around, doing nothing and waiting – for an idea, for frustration to goad you into action, for some small shift in the atmosphere or for the light that sets the mind free. Ask any writer how much time is spent staring at the wall, looking out of the window, arse-scratching and prevaricating. A lot of visual art – and of writing and perhaps music, too – reflects on this, and even uses it as the basis of a work itself. Unlike the sculptor's studio, with its piles of materials, equipment and bustling assistants, drawings are mostly made seated alone at a table in a room, in introspective quiet. In Whiteread's art, the room is where things begin – and where the world starts to writhe.