The artist and the subject of a portrait form a bond like no other. It may come about by chance, perhaps even covertly, with a quick sketch made in passing, or formally, over a series of arranged sittings. Whatever the occasion, the two are then bound together by the portrait.

This summer Stanley Tucci’s latest film as a director, Final Portrait, will attempt to reproduce the intensity of such an encounter. Starring Geoffrey Rush as Alberto Giacometti, it tells the story of the great Swiss artist’s attempt to paint a likeness of his friend, the American writer James Lord. The creative process ahead, a flattered Lord is assured, will only take a few hours. What follows, in Tucci’s careful cinematic treatment of Giacometti’s endeavour, is an entertaining collision of two world views, a kind of duel between the sitter and the artist, as the endlessly deferred completion of the portrait takes over their lives.

The film’s release in August will come in the wake of a groundbreaking new show at London’s National Portrait Gallery called The Encounter: Drawings from Leonardo to Rembrandt. Opening on Thursday, the exhibition uses a selection of 50 studies and sketches, some of great men and women and some of unknown associates and strangers, to set out a history of the craft of portraiture as practised by the European old masters. It includes Holbein’s ink-and-watercolour depiction of Henry VIII with Henry VII from around 1536-37, as well as sketches not seen for decades of shoemakers and artists’ apprentices, each chosen for the sense of connection they capture.

“Some of the drawings were perhaps never intended to leave the artists’ studios, but are arguably among the most engaging and powerful impressions of personal likeness in the history of art,” said Nicholas Cullinan, director of the gallery.

The drawings are all on loan from British collections: Albrecht Dürer’s preparatory study for a lost portrait of Henry Parker, Lord Morley, is from the British Museum, and some drawings from the Carracci studio in Bologna have been lent by Chatsworth House. There are 15 drawings from the Queen’s Royal Collection, including eight by Hans Holbein the Younger.

By the 18th century, Britain had become a centre for this form of art. David Piper’s seminal 1957 book The English Face reports a Swiss miniaturist commenting in 1755: “How fond the English are of having their portraits drawn.” The national obsession left a great legacy of work by artists from all over Europe. The results are not always flattering, nor are they intended to be. But whether they are in chalks or done with metalpoint, they are all attempts to unite notional objectivity with what the artist believes about form.

“These are not the kind of people you see in formal portraits, and some of the drawings, such as Carlo Dolci’s drawing of a shoemaker, hint at a less conventional transaction. Perhaps it was drawn in exchange for some shoe repairs,” said Tarnya Cooper, curatorial director of the gallery. “With a sketch by Pisanello, we can see he has used the face of an apprentice in the pose of a hanged man.”

Cooper’s co-curator, Charlotte Bolland, also points out how groups of artists, such as the Carracci cousins in Bologna, all influenced each other’s style. Another work in the show, Perugino’s Florentine Woman, reveals how a sketch of an informal sitter allowed an artist to create a more intimate, less idealised image.

Handily and by design, the exhibition runs next door to the BP Portrait Award show, which offers a quick update on contemporary practice. This year’s prize went to Benjamin Sullivan for his moody and arresting oil on canvas Breech!, which shows his wife Virginia breastfeeding their eight-month-old daughter, Edith. Sullivan, who lives and works in Suffolk, saw off competition from 2,580 entrants from 87 countries and often paints family members, believing “the emotional connection between sitter and artist is at the root of all successful portraits”. He said he wanted the portrait to celebrate a calm moment that had “descended after the usual period of disarrangement that new parents face”. In fact, it was made not in a moment, but over four to five weeks, as the couple recovered from what had been a difficult birth.

The acclaimed royal portraitist Michael Noakes has watched changing fashions in official commissions for 60 years. His sittings have often involved subtle negotiations, but some have resulted in friendships.

“It is not an equivalent to writing a biography, of course, because you have so much less time and that is not really what you want. But quite often I find my first judgment about someone is the one I come back to,” said Noakes, 83, who has four commissions awaiting him this year.

As a young artist in the 1960s, Noakes accepted an invitation to join the Royal Society of Portrait Painters, an organisation then looked down on by some of his peers, who thought portraiture too fawning a discipline.

“But I wanted to earn my living from art and I knew a great number of trained artists, even quite grand Royal Academicians, who had to teach to make any money. Teaching, I know, is a valuable contribution, but I wanted to paint. I have never wanted to be cruel to my subjects, but after painting hundreds of portraits I have probably tilted in both directions, towards flattery and cruelty, at times.”

Noakes has four works in the gallery: oil paintings of actor and raconteur Robert Morley, of writer JB Priestley, and of actors Margaret Rutherford and Ralph Richardson. “I told Richardson I didn’t let people look at my work in progress. ‘Oh, yes, absolutely’, he said, and then the minute I moved from my easel he came over to look.”

He remembers Rutherford more fondly. “She was charming, although losing it a little after a stroke. To make conversation, I asked when she got her Oscar. ‘I don’t know. Last Thursday, I think,’ she said.”

Noakes always works alone with his sitters, but when Rutherford’s painting was finished, he unveiled it to the actor and her husband, Stringer Davis. “Stringer said, ‘This is the happiest day of our lives’. It was lovely.”

For portrait painter Henry Mee, a decline in commissioned portraiture is a loss to historians. “Our digital age may leave little trace for future generations. There will be no dusty boxes of Victorian glass-plate, silver nitrate photographs in the loft, though the record of the way sitters contemplate their painters today may be as important for future historians as is Goya’s Family of Charles IV for our own understanding.”

Mee, who painted Princess Diana as well as the Queen, feels his task is to recreate an experience on canvas, complete with the fall of the light. “When the canvas looks and feels as if it has the aura and presence of the person in the room, the painting is complete. Recognition of, and understanding of, the person being painted is crucial. The painting is not a still life. The process of being painted is of consequence.”

The first images of monarchs and nobles were their marble or stone effigies on tombs – a mark of social status. With the Renaissance, portraiture became as much about the painter’s personal vision. Finally, in the 19th century, with the coming of photography, a merely fleeting relationship could result in an image.

A study from 2008 suggested, rather disappointingly, that portraiture is more of a display of ego than a truly reciprocal encounter. The art historian Simon Abrahams argued that artists tend to make their subjects look like themselves. His contentious theory was based on computer-aided analysis and claimed to show that painters could not help but portray themselves.

“At least two contemporaries of Peter Lely complained that the faces in his portraits resembled each other,” wrote Abrahams, “one even suggesting that he was too fond of studying his own features.”

Yet for Mee, “the highest, and ultimately the most important, art” is still portraiture.

“This interaction between painter and sitter is part of the human condition,” he said. “It’s our hedging against the figure of Time, with his hourglass and scythe.”