Offer Waterman, London, 25 September – 23 October 2015

David Hockney RA makes drawing look easy. Applying a few pen lines to paper, he somehow manages to capture the personality, quirks and mood of his subject. It’s a rare talent he’s had right from the start, as this exhibition of his early drawings proves. Dating from 1961, when the Bridlington-born artist was studying at the Royal College of Art, through to the late 1970s, when he settled in Los Angeles, the works on show include experimental sketches, intimate portraits of friends, and the celebrated series of prints, The Rake’s Progress.

ICA, London, 24 September – 15 November 2015

Prem Sahib’s work explores intimacy, sexuality and community, in particular the spaces that act as meeting places for gay communities within London, Berlin and beyond: clubs, cruising spots, and the internet. Creating performances, objects and installations, the up-and-coming artist is also involved with various club nights, including Anal House Meltdown, which he co-runs with artistic peers Eddie Peake and George Henry Longly. His first institutional solo exhibition in London opens at the ICA this week. (Prem Sahib and Eddie Peake discuss each other’s work in this feature).

British Museum, London, 24 September – 31 January 2016

First recorded in 500 BC, this fascinating exhibition explores the evolving meanings associated with the word Celtic, revealing how a common artistic style – rather than nationality or language – has connected the Celtic peoples over 2,500 years. Featuring breathtaking objects – including the incredible Gundestrup Cauldron (below), a silver vessel thought to date between 200 BC and 300 AD, intricately decorated with images of wild animals, Gods and Godesses – this is a major show, not to be missed.

A National Trust celebration of Brutalist architecture, London, Sheffield & Norwich, 25 September – 4 October 2015

Having been dismissed and attacked for decades, the Brutalist architecture of Britain is finally receiving some love. For ten days, the National Trust (an organization usually associated with country houses, rather than concrete) is running a series of tours around the nation’s Brutalist landmarks: the Southbank Centre in London, the Park Hill Estate in Sheffield and the University of East Anglia in Norwich.

Foundling Museum, London, 25 September – 2 January 2016

In the nineteenth century, unmarried women who lost their “chastity” faced being outcast from society, resulting in homelessness, unemployment, prostitution and even suicide. The so-called “fallen” woman became a popular figure in Victorian culture, mythologized as a warning to others. During this time the Foundling Hospital changed its admission process to focus on restoring respectability to the mothers who came to them, only offering assistance to previously “respectable” women. This exhibition features paintings by Dante Gabriel Rossetti, Richard Redgrave, George Frederic Watts and Thomas Faed, contextualizing them alongside the stories of Victorian women who pleaded with the Foundling Hospital to take their illegitimate babies into care, and a specially-commissioned sound installation from musician and composer, Steve Lewinson.

Ambika P3, London, 26 September – 11 October 2015

Martina Amati is an artist, filmmaker and amateur freediver, able to descend 30 meters below the surface of the ocean on a single breath. Under is a multi-screen installation which immerses viewers in the freediving experience – described by Amati as “a form of meditation” – giving them the sensation of being submerged beneath the water as they gaze up at a large screen above their heads.

Life: The Gallery, Surrey, 30 September – 10 January 2016

Best known for his vibrant, colourful, Matisse-inspired oil paintings of landscapes, flowers and people, Philip Sutton RA is also a skilled printmaker. In the 1970s he travelled to Fiji, where he gouged out designs on wooden boards to be printed on his return home. An exhibition of his woodcuts from this period opens at Life gallery this week. A special lunch with the artist will be hosted by Great Fosters hotel in Surrey on 1 October (for details email gallery@lifethegallery.com).

Anna Coatman (@AnnaCoatman) is Assistant Editor of RA Magazine.