There are over 12,000 paintings scattered throughout the National Trust’s many properties. That’s more than four times as many as owned by the National Gallery and nearly double the size of the Royal Collection.

But this remarkable horde, which includes major works by Titian, Velazquez, Van Dyck, Reynolds and Gainsborough, is, as the Trust’s chief curator David Taylor points out, “hidden in plain sight”. Many of the pictures are hard to see –tucked away in dark corners and set back in roped-off areas – or perhaps simply not a priority for visitors who are more interested in a Downton Abbey experience than the appreciation of Old Masters. And, let's be honest, hanging in those opulent interiors are many dull portraits of dull families, of interest only because of their associations with the house in question.

But there are also some absolute gems. Prized Possessions, which has just opened at the Holburne Museum in Bath, aims to shine a new light on a particular highlight of the collection. The curators have selected 22 paintings from the Dutch Golden Age, drawn from 13 National Trust houses – to create a glittering snapshot of the sheer quality, subtly and variety of the 17th-century painters.

From about 1620 until 1700, an explosion of wealth in the low countries fuelled a boom which was arguably without precedent in the history of art. The affluent merchants of the trading cities such as Amsterdam, Utrecht, Delft and Dordrecht bought paintings on an extraordinary scale, lining the walls of their new canal houses with landscapes, seascapes, portraits, narrative scenes ranging from high moral seriousness to low comedy, and – a particular enthusiasm – still lifes of astonishing precision.

A Still Life of Flowers and Fruit arranged on a Stone Plinth in a Garden by Cornelis de Heem, mid 1680s Credit: National Trust

Part of the point of the selection on show at the Holburne is to illustrate exactly that variety. A Rembrandt self-portrait from Buckland Abbey hangs on the same wall as seduction scenes laden with innuendo by Jan Steen, Gabriel Metsu (both from Upton House) and Gerard ter Borch (Polesden Lacey). They are framed by the silent, light-filled interior of a Utrecht church by Saendrenham and de Hooch’s atmospheric evocation of childhood mischief Colf Players.

In the next gallery a tiny minimalist still life of a blackbird pecking at cherries hangs opposite a cornucopia of luxuriant flowers and fruit by de Heem. When it comes to seascapes, a wonderful panorama of a naval battle full of smoke and canon fire by Willem van der Velde from Felbrigg Hall, is about as far removed as you could get from Cuyp’s luminescent view across the water to Dordrecht on a still summer evening – one of his greatest paintings, on loan from Ascott House.

A Magus at a Table by Jan Lievens, circa 1631/2 Credit: National Trust

But the exhibition gives us more than an at-a-glance overview of the Golden Age. It also reveals much about the British relationship with 17th-century Dutch paintings, which were part of the original decorative schemes at both Ham House and Dyrham Park. Certainly, their appeal to the owners of country houses throughout Britain has endured almost without interruption. The Sea Battle was bought for Felbrigg Hall in 1752, and Anthony de Rothschild bought the Cuyp for Ascott in 1924, while the Rembrandt was gifted to the Trust as recently as 2010.

With only 22 paintings on show, you might not feel inclined to make a long journey to Bath to see this exhibition. But, if you are nearby, or going anyway, you won’t find a more succinct and approachable overview of one of the great moments in western art. And if you miss it in Bath, the show travels to the Mauritshuis in The Hague in October and then to the NT's own Petworth House in January 2019 – a reminder that the Trust has the capacity to showcase exhibitions like this in its own properties, and has the potential to do much more with its collections.

Prized Possessions: Dutch Paintings from National Trust Housesis at the Holburne Museum, Bath until September 16 holburne.org 01225 388569