VISITORS to Venice, the not-so-grand tourists de nos jours, come to enjoy the wealth of Titians, Tintorettos, and Veroneses in any number of churches and museums, as well as in the Palazzo Ducale. Private mansions house the later collections of Tiepolos, Longhis, and Piazzettas, often in buildings unchanged since a riot of rococo overtook the interior designers. Since the 16th century, European travellers have collected such works assiduously, as many country houses in the UK bear witness.

It might seem perverse, therefore, to go to Venice to see paintings and works of art from other parts of the Italian peninsula, but any member of the congregation leaving the English Church comes out on to the Campo San Vio, named after the long-demolished Church of Santi Vito e Modesto. Opposite, to the west of the little bridge, stands the Palazzo Cini with one such superlative collection.

When I was locum Anglican Chaplain one winter, the palace across the way was always shuttered; more recently, the collection, first opened to the public in 1984 by Cini's heirs, has been closed for rearrangement and restoration. It will now be open for at least six months each year as part of the city's "Museum Mile", which leads from the Accademia to the collections of Peggy Guggenheim and the Seminary, and the contemporary gallery of the Punta della Dogana.

Here one gets to see choice works attributed to Piero della Francesca, Filippo Lippi, Botticelli, and the Tuscan Mannerist painter Pontormo. When I attended the opening, Pontormo's outstanding double portrait of two friends was still on loan, one of the highlights of the exhibition in the Palazzo Strozzi (Arts, 30 May). To these has been added a selection of works from Ferrara which had been in storage since 1989; Cosmè Tura, Ercole de' Roberti, Marco Zoppa, and some surprising compositions from Ludovico Mazzolino (1480-1528).

The palace was formed in the 1920s, by knocking together two former medieval homes for the industrialist Vittorio Cini, who was born in Ferrara, and his wife, the silent-movie starlet Lyda Borelli. Much later, in the mid-1950s, they employed the architect Tomaso Buzzi to redesign the layout of the two houses.

A steep oval stairwell (1956-58) gracefully captures the spirit of Andrea Palladio (the Venetian Church of Santa Maria della Carità), Vignola (the palace at Caprarola), and Borromini, while a discreetly enclosed oval dining-room in neo-rococo style replaced a redundant staircase in the centre of the palace. It is lined with 275 pieces of soft-paste porcelain from the last years of the Venetian Republic manufactured by Geminiano Cozzi's San Giobbe factory (1785-95), which fired seven kilns until it was closed down by Napoleon.

These white porcelain dishes, verrières and jardinières, and the earlier enamelled copper dishes and mirrors, constitute the only glimpses of Venetian art in this priceless collection, which begins with early-medieval Christian art and concludes with a flourish in the Renaissance.

Dominated by a mid-13th-century double-sided processional cross, the first room holds later French and Sicilian ivory bas-reliefs from portable altars and diptychs, their delicate incisive forms alive with a world in miniature.

The painted cross itself, from the circle of Giunto Pisano, shows the suffering Christ on one side and a Christ Triumphant on the reverse. Both figures are sinuous and identical in all but the angle at which the Saviour holds his head. The pathos of seeing this pass in procession must have reminded the believer of the ultimate cost of discipleship and the promise of risen life.

Among the so-called "Primitives" of the Gothic school that the art-historians-cum-dealers Bernard Berenson and Federico Zeri persuaded Cini to buy is a central-Italian Madonna and Child in the type known as the Sedes Sapientiae, in which the Mother of God is depicted on the seat of Divine Wisdom. Her son, already with manly features, holds the scroll of the Law in his left hand while offering a blessing with his right.

In this room, formerly a dining-room with a large Murano glass chandelier and clever contemporary lamp stands, are also several masterpieces of Sienese work. These include a Maestà (by the Master of Badia a Isola), in which the Virgin is seated with her son and surrounded by four attentive angels, and an impassive Madonna and Child by Niccolò di Segna (active around 1331 to 1345), in which the inquisitive Christ Child tugs at the Virgin's headscarf to encourage us to look upon her face of compassion.

The largest room on this floor, which gives on to the oval dining-room, is flooded by light from outside where the Anglican church lies below, making it difficult to see the statuary standing between the windows. The metre-and-a-half-tall Madonna and Child is here credited to the circle of Francesco di Valdambrino (died 1435), a sculptor from Siena whose work tiptoes towards the springtime of the Florentine Renaissance itself. He had worked for the Duomo in Florence. This pitying Virgin, her right hand raised to signify phatic utterance, as if to proclaim him whom she holds in her left arm, might have graced an altar there.

The largest works in the room are two polyptychs, one of St Paul from the Church of St Catherine in Pisa, standing above a chestnut-wood marriage chest inlaid with an idealised cityscape, and, facing it, one dated 1404 of the Virgin and Child with Sts Anthony Abbot, Laurence, Agatha, and John the Baptist.

Among the wealth of Renaissance pictures in the corner room are works by Beato Angelico (a single panel from a broken-up polyptych of St Thomas Aquinas, quill in hand, as he stands on a cloud awaiting heavenly dictation), a roundel by the Florentine Domenico Ghirlandaio, and Piero di Cosimo's extraordinary Madonna and Child with Two Musician Angels, a work Cini found in the antique markets of Florence in 1957.

In it, the infant tries to tug away the bow from the adolescent angel who is tuning his rebec, while, behind the group, another angel is studying his music, and the whole is a joyful celebration of the celestial harmony that Christ alone can bring. Piero (1462-1521) painted this most probably in the second decade of the 16th century, no doubt influenced both by seeing paintings by Da Vinci and engravings and woodcuts by Dürer.

But it is to another Piero that visitors will wish to turn. I hope that communicants leaving divine service at St George's will be the first among many to enter the new treasure house that the Fondazione Cini has reopened to the city, as I can imagine no better place to give thanks after making one's communion than in the silence of the Villamarina Madonna.

Neither figure stands in our lifetime, nor in our world, and yet both invite us to join them, and it is this "heaven-in-earth" quality that encourages me to think that the attribution to Piero is still likely. Berenson argued, against Zeri, that it was an early work by Luca Signorelli, and the debate continues, but not so noisily as to assault our ears or interrupt our prayers.

"Tuscan and Ferrarese Masterpieces from the Collection of Vittorio Cini" is at Palazzo Cini, Dorsoduro 864, San Vio, Venice, until 2 November.

Phone 00 39 041 241 1281.
www.palazzocini.it