Antony Van Dyck is the Mozart of painting: a perfect miracle of form combined with rich and glowing statements in portraiture that capture and express life in a limitless and elegant way. He is among the ten greatest artists the world has ever produced. His own age recognised this. Artistically the most discerning king on any European throne at the beginning of the seventeenth century, Charles I, was his greatest patron, but others, like Philip of Spain, were after him.

Time was short. Van Dyck lived only 41 years. He arrived first in London in 1620, and for some mysterious and unexplained reason left again shortly after that, returning in 1632 and spending much of the nine years left to him painting portraits that changed the direction and stature of this wonderful art form.

Some of the most glorious examples are included in Van Dyck and Britain, an exhibition recently opened at Tate Britain on Millbank. It features a fine work called The Greate Peece’, his first big commission for the King, showing Charles I and his French wife, Henrietta Maria with their two eldest children. The King wanted the man who was to become his favourite painter to project an image of majesty, rivalling the artistic pretensions of other European monarchs and this Van Dyck willingly achieved. But he trumped it by showing also the loving family relationship that the king enjoyed and the calm and happiness that surrounded him in his private life among his eight children.

He was rewarded with a knighthood and the gift of a house on the Thames where the King used to come down on private visits in the royal barge.

Van Dyck achieved a parallel success with portraits of courtiers and men of power like Thomas Wentworth, Earl of Strafford, the despotic ruler of Ireland as lord deputy and then lord lieutenant. Twice portrayed in this show, the strength and determination of this man, who became chief adviser to the king, is amply demonstrated.

Van Dyck’s was a fleeting moment of time. Many of those he portrayed were swept away. Wentworth was beheaded as was the king. But the images lived on to inspire generations of artists. The last two rooms should be ignored. They try to show the influence after Van Dyck but it does not work. He stands, like Mozart, alone in his lasting glory.

From Tate Britain you can take a twenty-minute boat journey down the Thames to Tate Modern. It is the quickest way to make the journey. On a February day of matchless, brilliant sunshine, with the buildings spread out from Millbank to St Paul’s Cathedral, it is the easiest and only way to travel. And in the vast modern museum, so successfully made out of a power station, can be seen a remarkable exhibition of Russian Constructivism featuring its two greatest exponents, Liubov Popova (1889-1924) and Aleksandr Rodchenko (1891-1956). They were part of the Russian Revolution, founding their movement in the midst of revolutionary turmoil.

What they did was part of the transition of art from Cubism to Abstraction. Their work influenced Mainie Jellett and Albert Gleizes in their researches and helped form the remarkable movement in art in the period 1917-1924 that was to shape painting throughout the twentieth century, just as Van Dyck had done with portraiture during his short career in the early seventeenth century.

Popova and Rodchenko enmeshed their lives in the life of the nascent union of Soviets. They involved themselves in everything useful and life-giving – theatre, science, invention, textile and fashion design, while at the same time exploring the nature of form in art and its non-objective representation.

Their rich gift to the Russian people was checked by Stalin. He wanted a different form of art, called ‘Heroic Realism’ – we could do with a bit here at the moment – that glorified the workers and the peasants. It became hypocritical. Having made these people heroic Stalin then sent them to the Gulag or simply murdered them in millions. Popova died; Rodchenko was marginalised and turned to film-making. Socialist Realism was the only approved art form and it succeeded in marginalising art itself throughout the Soviet Union.

More Van Dyck’s were to be seen on a day trip to Windsor Castle, a chance to look at the world’s greatest art collection hanging in normal, family circumstances, though what a family! The Queen, unsurprisingly, has a plentiful supply of Van Dycks, including two that are in show at the Tate – the equestrian portrait of the King and the delicious Cupid and Psyche, in which Psyche, modelled by Van Dyck’s mistress, her body barely covered with the end of a scarf, lies sleeping on a bank as Cupid gazes in rapture at her.

In the Royal Academy there are two important shows, one on the Italian Renaissance architect, Palladio, the other on Byzantium. Small, but with brilliantly gathered artefacts including some outstanding architectural models of work by Palladio – who was Michelangelo’s contemporary – and sixth century works from the Byzantine Empire,

Arthur Miller’s A View from the Bridge, at the Duke of York’s Theatre in St Martin’s Lane, is a fine production of a wonderful tragedy about jealousy. Ken Stott plays Eddie Carbone, the anger in the character pulsating against Rodolpho, the Italian who has entered the United States illegally and won the heart of the longshoreman’s niece, Catherine, played by Hayley Atwell. Eddie’s wife, Beatrice, played by Mary Elizabeth Mastrantonio, and his lawyer, Alfiero, played by Alan Corduner, look on helplessly as he destroys himself.

The playing by the two women is singularly good. Stott is too angry and has insufficient nobility. I was reminded of Godfrey Quigley in the part, many years ago, and felt Stott did not come up to the earlier performance. That is a sea-change in theatre that would need much space to explore. The excellent play by Miller rounded off a memorable London week.