Some of these "strangers" were visitors, like Holbein and Van Dyck, but many settled here and became naturalised Englishmen or "denizens". They brought an invigorating new range of techniques that transformed English art. Most of the paintings and drawings on show here are portraits, but the exhibition is not the dour gallery of Tudor mug-shots that this might suggest. They come in a marvellous variety of styles, and in all shapes and sizes, from the fastidious miniatures of Hilliard and Isaac Oliver, painted on two-inch snippets of vellum glued to bits of playing-card, to the tall, lush, overbearing canvases of Stuart court artists.
There is also a variety of ideas as to what a portrait is, and what it should say about its subject. We see here, as Karen Hearn says in her catalogue, "an ebb and flow in the desire for naturalistic representation". Among the earliest works are exquisite Holbein sketches from the 1530s, where every hair on a young woman's eyebrows seems alive, but for much of the Tudor period the capturing of physical and personal detail seems almost incidental. The portrait is seen more as a mode of display, a finely tuned statement of the sitter's status and allegiance, a creating of his or her "image" in the public relations sense of the word we use today.
These are pictures to be read as much as viewed, their messages signalled in costume details, Latin mottoes and heraldic devices, and in a range of symbolic props in which everything from gillyflowers to goldfinches has an emblematic meaning.
The chief "dynasties" portrayed here are the Tudors and Stuarts, but there is a powerful presence of those other great English families - aristocrats, arrivistes, merchants, politicians - whose flair, energy and greed were as decisive in the history of the period as the policies of the monarchs themselves.
One of the most arresting pictures is the Cobham family portrait. Painted in 1567 by an unnamed artist in the service of the Countess of Warwick, it shows William Brooke, 10th Lord Cobham, at the age of about 40, together with his wife and sister, his six young children, and their assorted pets. It is mealtime, specifically dessert: a scene of domestic togetherness, but painted with that deliberate waxy stiffness, that sense of ceremonial hush, which takes one away from the everyday and into the realm of the painting's messages and meanings.
The message is precisely dynastic. The Latin inscription compares Lord Cobham to Old Testament patriarchs like Jacob and Job. "God grant that the line of Cobham beget many offspring such as Joseph." The prayer is already answered by the clutch of doll-like children below; indeed the whole composition has the diagrammatic look of a family tree.
On the table there are fruit - apples, pears, grapes, walnuts: a tribute to the prolific orchards of Cobham Hall, and a restatement of the picture's message of fruitfulness and dynastic harvest. Another symbolic prop is the diamond pendant Lady Cobham wears, in the shape of an ocean-going ship. This suggests another kind of harvest: the riches of maritime trade filling the Cobham coffers. The parrot and the monkey - imported New World pets - are part of the same idea. The ship also has an emblematic meaning of happiness, alluding to a Roman emblem showing a ship named Felicitas.
The Cobham portrait seems almost a kind of talisman, an invoking of familial health, wealth and stability in an age of slippery fortunes. In fact, there are historical ironies to the picture. The title was inherited by Henry, seen here as a two-year-old with a puppy on his lap. Implicated in a conspiracy against King James in 1603, he was attainted for treason and stripped of his peerage, thus bringing to an abrupt end the dynastic aspirations expressed in this painting.
We catch the Cobhams in a moment of eminence which proves somewhat temporary. Portraits of the Catholic Howards have a similar resonance, particularly the canvas of the Earl of Surrey, the nobleman-poet, bursting with confidence and Italianate elegance. It was painted in 1546, when he was 29; a year later he was beheaded on a trumped-up charge of treason.
The Brookes and the Howards were powerful but expendable satellites around the central dynasty of the monarchy. Royal portraits form the heart of the exhibition. The earliest (c 1500) is the poignant little portrait of Prince Arthur, Henry VIII's elder brother, who died at the age of 15. This was rediscovered a couple of years ago, at Castle Forbes in Ireland, and is seen here for the first time.
An entire room is devoted to images of Queen Elizabeth. She was the most cultish of all the Tudors, and fully exploited the propagandist element of portraiture. Most of the surviving pictures of her are known by some symbolic device or allusion. Here we have the "Armada portrait", and the rather ghostly "Sieve portrait". The most striking is the "Phoenix portrait" (c 1576) attributed to Hilliard, though it is not the symbolic paraphernalia that catches the eye - the phoenix jewel and the Tudor rose - but the brilliant detail of Hilliard's workmanship. The gold embroidery of the dress is represented by paint, principally lead-tin yellow, rather than by the actual gold leaf used a generation earlier (for example, in the 1544 portrait of Mary Tudor). This kind of technical advance contributed to the growing autonomy of the artist, enabling him to represent precious materials without having to afford them.
The portraits of Elizabeth do not invite personal or biographical interpretations, but the study of King James, by the Dutchman Adrian Vanson, certainly does. Painted in 1595, it shows a very human James at the age of 29 (though some of its unusual intimacy is a result of a later cutting-down of the picture). The face is sallow, the gaze weary, the mouth thin and ironic. One thinks of the personal traumas of his childhood: the murders, the night flights, the execution of his mother. He seems slightly slumped. His tall sugar-loaf hat is tipped back, giving him the air of a melancholy young boulevardier resting between bouts of absinthe.
Right beside this is a portrait of the wily Sir Robert Cecil, painted by De Critz in about 1602, on the eve of James's succession to the English throne, which Cecil as Secretary of State had done so much to engineer. Here is a man in control of his own destiny - far more so, one feels, than the droopy young king next door. On his table are folded dispatches, a seal-bag, a bell to summon his amanuenses and clerks. This is the new man, the bureaucrat, the political string-puller.
In the portraits of Cobham and Cecil, and in the lesser-known merchants and gentry staring huffily out, one gets a sombre, mafia-like sense of Elizabethan power- mongering. But there is plenty of the more flamboyant side, the peacockery and swagger, as in Hilliard's famous miniature of George Clifford, 3rd Earl of Cumberland, in an extravagant costume of azure and gold embroidered with astrological and alchemical devices. He is dressed up for the Accession Day Tilt, a mock-chivalric festival in which aspiring courtiers jousted for the Queen's favours.
Cumberland - an inveterate gambler and a courageous sea-captain - epitomises the panache of the era. Even more eyecatching is Richard Sackville, 3rd Earl of Dorset, painted by William Larkin in "cloth of silver embroidered all over in slips of satin, black and gold". He is the perfect dandy, from his doily-like ruff down to his pom-pommed pantouffles. This probably shows him at the wedding of Princess Elizabeth and the Elector Palatine, 14 February 1613, at which it was said he "dazzled the eyes of all who saw".
Among all the monarchs and magnates are a few pictures of the artists themselves. Easily missed is the wry self-portrait by George Gower (1579). It is the only large-size self-portrait in existence by a 16th-century British artist. He holds a palette and a paintbrush. An inscription celebrates his work "by pencil's trade" and the rewards it has brought him: "What parents bore by just renown, my skill maintains."
And so a new professional group edges up the increasingly crowded and competitive social ladder. Essentially of artisan class - servers of apprenticeship, members of guilds, guarders of trade secrets - they have acquired an indispensable role as the image-makers of Tudor high society.
n 'Dynasties: Painting in Tudor and Jacobean England 1530-1630' is at the Tate Gallery, London SW1 to 7 Jan 1996 (0171-887 8000)
n Charles Nicholl is the author of 'The Reckoning: The Murder of Christopher Marlowe', Picador pounds 7.99, and 'The Creature in the Map', Cape, pounds 18.99. He will be participating in an international symposium on 'Dynasties' at the Tate Gallery, 30 Nov-1 Dec; (details: 0171-887 8758)