40 x 50 cm Oil on canvas. Monet's Woman in a Garden painted by Kamila Figler! For sale! Interested? It's better get the painting before I graduate, because you might not afford it when I will become a famous artist;)

Is there any conglomerate structure in Visual Arts industry in the United Kingdom?

1. Map of the ownership structure of content producers.

There are a few groups that play more important role in the Art Industry.
For instance, the British Council Arts group develops innovative events and collaborations that link thousands of artists and cultural institutions around the world, drawing them into a closer relationship with the UK.
The Royal Photographic Society Visual Arts Group links all fans of photography and art,
The Scottish Visual Arts group focuses on museums, galleries and other organisations as well as individuals associated with archives, records or collections related to the visual arts.
The Art Group is a market leader in contemporary art publishing.
For over 20 years we’ve been working with thousands of artists to
supply quality wall art, cards and frames to a global market.
The London Group is an artists’ exhibiting society based in London, England, founded in 1913.
There is also Voluntary Arts Network which aims to increase participation in the arts, and its local part,Voluntary Arts England.

You can also take a look at the map I posted here.

2. Which are the conglomerates behind the content producers?

Well, It is quite hard to find any conglomerate in the Visual Arts Industry in United Kingdom, mostly because most of the content producers are the artists or photographers who work as freelancers. Many of them have their websites, some of them have their agencies or companies, like for example Electronic Arts which specializes rather in production of the computer games.

Leading Light Conceptual Design Ltd, based in Surrey, is a UK company specializing in Concept Art and Production design for the Entertainment industry. They produce Art content for, among others, the conglomerates such as EA Games, Microsoft Games Studios, Sony, Fujitsu and BBC Two.

After some research I found an useful website! ArtsAccessUK.org is an access guide for the UK Arts.
You can find artforms like: Architecture, crafts, Combined Arts, Dance, Design, Digital content, Drama, Education/training, Festival, Film/Video, Heritage, Installation/Live Art/Performance Art,Public Art or Street arts/carnival. In the areas: all of UK, Northern Ireland, Scotland, Wales, East Midlands, Greater London…

3. How big is the share not owned by UK companies?
Well, the Art Industry is enormous! According to ARTFACTS.NET There are (attention!) 240,192 Visual Artists and 19905 Art institutions worldwide!
As Louise Nevelson once said:

Art is everywhere, except it has to pass through a creative mind.

4. What are the effects of these conglomerates on cultural production and society?
I think that in case of Art industry, conglomerates are not as influencial as single independent artists, whose names became famous. Generally I noticed the trend that the higher status of a social class, the greater is the need for original, famous paintings. Modern society looks for the meaning in art. Shocking images can became famous sooner that other ones. To influence a cultural production an artist must come with a new idea or present something in a different way in order to make his art unique and popular.

Art is not what you see, but what you make others see.– Edgar Degas