A lifesize trompe l’oeil painting of the real-life lift at Camden Arts Centre opens this exhibition by the Canadian artist Allison Katz. Its doors are agape, revealing a deep silver box within. Its metal sheen gives the work a sense of photorealism, but it’s the 3D depth that implores you to step inside. It’s a fitting welcome for a show entitled Artery; the lift instantly stirs up thoughts of transportation, liminality and portals.

Katz, 41, was born in Montreal and now lives in London. Her whimsical work, thematically fluid and exploring the conventions of traditional painting, has seen her become a rising figure in contemporary art. She was shortlisted for the Max Mara art prize for women in 2020 and featured in last year’s acclaimed Mixing It Up: Painting Today show at the Hayward Gallery. Artery, previously at Nottingham Contemporary, is Katz’s first solo UK exhibition, and arrives with bags full of her favourite recurring tropes and motifs: monkeys, eggs and more.

Katz has a thing about cockerels. In The Cockfather, a chicken’s body has been restructured to the shape of a dish that holds three eggs, a comical rumination. There are also lots of cabbages. She paints them in varying luminous green shades and sits them upright on tables. At the side of each veiny vegetable is the silhouette of a man’s face. They’re pretty images, but the joke is in working out what they are. Are these actually still lifes or portraits of the artist’s shy partner?

Katz’s strange and mischievous storytelling recalls Paula Rego; the cabbage in The Artist in Her Studio by Rego comes to mind. Cabbages lack the pop-cultural currency of avocados, but they are significant in the history of painting. Leonora Carrington and Stanley Spencer both painted them. Perhaps this explains Katz’s interest?

There’s an inherent humour in Katz’s paintings; everything is glazed with a sense of trickery, works like banana peels waiting to trip you up. Blue and gold brushstrokes make a face, reminiscent of Matisse’s visage paintings, in Akgraph (Tobias + Angel), but closer inspection reveals that the eyes, nose and mouth spell out the word “mask” – Katz’s initials (Ms Allison Sarah Katz). A small dog, fish skeleton and birds encircle the face, all of which sit atop a foggy, reimagined Tobias and the Angel, a 15th-century altar painting by Andrea del Verrocchio.

Ceaselessly playing with illusion and perception, Katz’s dreamlike works exist somewhere between the fantastic and the familiar. Some paintings are detailed, like Posterchild, a collage of random images akin to the experience of online scrolling. Others are basic and unfussy, which can be jarring. Someone Else’s Dream, depicting a naked man in a field of bulls, feels unspirited and lacks the energy present in the surrounding works.

Katz is at her best when layering ideas. One series of works is painted from the vantage point of a throat, so that teeth and gums frame the subject. MASK is a self-portrait from a Miu Miu advert that Katz starred in last year. It’s interesting to see the mouth presented as a tool of observation.