The title of this career-long survey of political pieces by Richard Hamilton is something of a misnomer: for the most part, these aren't Protest Pictures at all. Sure, it's not hard to guess where on the political spectrum Hamilton's views lie, but the works on show at Inverleith House aren't tub-thumping, flag-waving calls to arms. They're much more subtle than that, ranging from ambiguous reportage to finely-tuned satire, via keen observation of the media's role in presenting and filtering ideas and ideals.

The show begins in 1967 with the Redlands case, when the Rolling Stones and art dealer Robert Fraser fell victim to a dubious drug bust. Hamilton focuses on a single image culled from a newspaper photograph of Fraser and Mick Jagger, handcuffed in the back of a black maria and shielding their faces from the press pack. The first of the repeated reworkings adds a coloured tint, the next borrows the style of court sketch artists. A poster work collects a scrapbook of cuttings on the Stones' court appearances. It remains unclear whether Hamilton is condemning this last-gasp attempt by a stuffy establishment to punish the figureheads of a new lifestyle, or coolly documenting the process.

Later versions of the scene, made in the early 1970s, seem to acknowledge Hamilton's own role in crafting an iconic image and see him acting as a seer, presaging the status of the scandal, like that later disaster for the Stones, Altamont, as a pop cultural turning point. In a pair of prints that borrow their title from a contemporary headline - A strong sweet smell of incense - Fraser and Jagger are obscured behind a layer of decaying celluloid, as if the image has been replayed over and over again. These are followed by a final commemoration, a screenprint that describes the scene in flat panels of bright colour, as if Hamilton is committing the lurid, gossipy tale to collective memory.

The Treatment Room, an installation dating to 1983, is chilling enough, and a clear condemnation of Thatcherism, but again Hamilton resists the urge to shout, preferring to whisper, however bitterly.

Occupying a room of its own, the walls painted in that familiar, queasy NHS green, the piece is a stylised radiography room, complete with bed, stool and protective screen. On the gantry where an X-ray machine is usually mounted, there is a television emitting a different kind of radiation, in the form of a party political broadcast by Margaret Thatcher.

Upstairs, still in the 1980s, comes a room dubbed The Troubles, dominated by three diptychs. The Subject shows a marching Orangeman set beside a blurred scene showing what might be headlights, or a riot in progress. Next, in a rusted frame, The Citizen is a Republican prisoner on hunger strike, the second panel blurring his dirty protest into near-abstract whorls. Last, in The State, a soldier, his weapon and camouflage uniform are precisely rendered, with real fabric pockets applied to the painting's surface, emphasisng the apparatus over the man inside it. The power is in Hamilton's ability to present the situation in Northern Ireland from conflicting viewpoints: the titles veer between representing the paintings' subjects from their own point of view and that of outside observers; and the three works are doubly mediated, through Hamilton and through his source, a television documentary.

This tension between source material and finished work is explored again in the Kent State series. First come photographs of TV footage of the campus anti-war protest of 1970 and the National Guard retaliation, which resulted in the death of four students. Next, a series of 12 proofs of a screenprint based on contemporary footage, which begin with a pale blue ground, and end with the image of a student lying prone. Then, the finished print, with a 13th stencil applied to reveal bright red bloodstains on the student's body. A coda of sorts comes in a pastel drawing, rendering the scene in hallucinatory bursts of colour, with loose lines suggesting a sort of moral heat haze.

The show closes with a new work, Shock and Awe, which casts Tony Blair, done up as an avenging cowboy, both hands on his six guns, ready to draw. Behind him, the sky is a post-apocalyptic red, and oil fires rage. That might sound trite, but even when he appears to be making a quick, cartoonish satirical jab, Hamilton hangs on to the subtlety and ambiguity that runs through his practice as a whole.

The head Hamilton has grafted on to a gunslinger's body isn't the boggle-eyed grimacing former PM of a Steve Bell strip, instead bearing a look that suggests Blair, beneath a half-hearted attempt at a steely glare, knows something has gone very wrong. He looks, aptly enough, like a man caught in a lie, trying to bluff his way out. It looks as if Hamilton is nodding in the direction of Warhol's silvery screenprint of Elvis, too, adding another layer of satire (or kicking a man when he's down), by reminding us of the days when Blair caught flak for nothing more than the minor, if cringeworthy, crime of hitching his wagon to Cool Britannia, posturing with his Fender Stratocaster and posing with Britpop stars.

Beside Hamilton's broadside against Blair hangs a series of works dating the early 1960s, revealing the artist has come full circle. Portrait of Hugh Gaitskell as a Famous Monster of Filmland attacks the then Labour leader for his policies in favour of nuclear deterrence - like Blair's Iraq adventure, a stance that hardly reflected the views of his party's rank and file - by layering a mask fashioned from B-movie bogeymen over Gaitskell's face. In combining Jack the Ripper, The Man with the Atom Brain and The Creature from the Black Lagoon, Hamilton casts his subject as a monster-villain, and predicts a mutant future should the Cold War powers test the doctrine of mutually-assured destruction.

There are one or two off-key notes here, as when an infographic of the first Gulf War is shown on a television dripping in blood, or posters protesting museum fees cast institutions as political prisoners, but in both cases, one suspects that Hamilton has an eyebrow raised. Those slips aside, though, this is an outstanding body of work, proof that, in the right hands, explicitly political art can rise above agit-prop or ham-fisted condemnation.

Richard Hamilton - Protest Pictures is at Inverleith House, Edinburgh, until October 12.