This exhibition focuses on nine visitors from North America, the South Pacific, Africa and India: all places with which Britain had a colonial relationship. The stories tell of a life displaced, sometimes temporarily, and of the reactions of London to this ‘other’.

Each of the nine is afforded a corner of the room, and a few paragraphs explaining their provenance and context. There's a large, usually oil on canvas portrait, and several smaller supporting images (from the press, caricatures, sketches and so on) and, in some cases, a small glass topped display case containing associated artefacts.

The first image is of Michael Alphonsus Shen Fu-Tsung, painted by famous British artist, Sir Godfrey Kneller. This large oil on canvas is entitled ‘the Chinese Convert’ and uses traditional European painting techniques to depict this change. Oddly lit, this sizeable image is difficult to see amidst the reflections on it, and it is also a little difficult to gather the importance of the image in introducing the exhibition.

Certainly there are stories here to be explored: often they are stories of imported individuals who participated in some kind of London-based charade. Some came for the adventure, others by compulsion, others in order to gain some help or power in their place of origin. And there are features which distinguish these portraits: the use of European techniques to depict non-Europeans; the combination of European and non-European dress in the paintings; the exploitation and power of portraiture.

But though this exhibition purports to explore these complex, authoritarian and ambiguous relationships, there's little to help us do so. It often feels like a list rather than anything more. No serious attempt is made to link the experiences of the thirteen. And it relies heavily on the accompanying paragraphs for context, though even these are thin overviews. Other potted lives include William Anah Sessarakoo, whose story inspired Aphra Behn's Oroonoko, Raja Rammohun Roy, the first Indian intellectual to sail to Britain - and Bennelong and Yemmerrawanne, Aboriginal Australians, brought to Britain by Governor Philip.

The only woman represented, Sara Baartman, hailed from Africa, and was literally put on public display in Piccadilly under the title ‘Hottentot Venus’, because of what was then described as ‘the enormous size of her posterior parts’. She was the focus of anti-slavery campaigners and coarse caricatures alike.

The exhibition shows some of these caricatures as well as a lithograph and posters announcing her appearance. The accompanying text declares that her story is “as horrifying to modern sensibilities as it was to some of her contemporaries.”

And this declaration addresses the central problem with the exhibition: most of the experiences listed here are a testimony to the long hand of colonialism. But the exhibition only gives an outline of the experiences of these visitors to London. Hence the dimensions of understanding on offer aren't much greater for us, than they were for the audiences for whom these pictures were first painted. The manner of the display has a dash of retro anthropology – note the glass topped display cases etc – which demands in return some authority and depth.

The viewer might want the curator to explore the idea that these lives are ciphers for the colonial experience - though one in which the displaced, colonised ‘subject’ enters the colonising universe, rather than the other way round. One might even wish for the notion of being ‘Between Worlds’ to be really meaningful – to speak of contexts, of the experience of being dislocated, of occupying neither a non-European nor European place, of belonging nowhere. Or indeed, of a more complex power dynamic in which the colonised subject tries to manipulate the dominant power.

But the viewer will be left wanting: wanting historical flesh on the bones of this story. Whilst gathering these pictures - which are usually scattered over several collections - was a promising exercise, this display still doesn't allow its sitters to speak. This is more than an oversight, it's a lost opportunity.

Learn more about the Between Worlds portraits online