Pillowy lamps, daybeds that look like stacked mattresses and rugs featuring abstract renderings of private body parts feature in an exhibition of new launches from Faye Toogood at Milan design week.

The Rude Arts Club showcase brings together products created by the British designer for rug company CC-Tapis and furniture brand Tacchini that explore sex and the human form from a female perspective.

"This is my take on embracing all that comes with being a woman," Toogood told Dezeen. "I'm a couple of years off being 50 and I spent the last 20-30 years in design not really drawing attention to being female."

"I'm a second-wave feminist," she added. "We were much more like: being female is not part of the conversation. We don't want to talk about it. We're just designers."

The collection of Rude rugs was born from impromptu paintings made by Toogood after visiting an exhibition of work by artist Francis Bacon, who made the human body his central subject.

"It got me thinking about the male interpretation of sexuality and the body," Toogood said. "And I thought, I'll have a go at doing that myself."

The designer initially suggested half as a joke that CC-Tapis should turn her "mischievous" paintings into rugs for their latest collaboration.

But co-founder Fabrizio Cantoni ran with the idea and produced one rug for each of the seven paintings, featuring abstract shapes reminiscent of breasts, ovaries and a three-pronged phallus.

"It's a kind of expression of the human body – male, female, everyone – but also the sexual energy that is a big part of being human," Toogood said.

Each rug was made using a different technique and different yarns, helping to translate the textural qualities of the different brush strokes.

"Normally when you do a collection, you pick your technique and then you run it across the five different designs," the designer said. "So this is pretty mega in terms of the amount of work and the amount of master craftsmanship it's taken to do this."

At the Rude Arts Club exhibition, the rugs are hung on the walls alonside the paintings themselves.

They provide a backdrop for Toogood's designs for Tacchini – the Solar daybeds and sofas, which are so plush they "feel like a cloud", and the Lunar lights and mirrors made of "scrunchable" white artists' canvas.

These offer a more subtle take on the theme, with soft curves and textures suggesting piles of pillows and mattresses as in the fairytale of the Princess and the Pea.

"Celebrating female energy and womanhood in design – and acknowledging it – is not something that personally I have done," Toogood said. "And I feel it's not something that the design industry has done either."

"There are still very few female designers that we all know about, talk about, write about," she added. "And there's not enough acknowledgement of female designers right at the top level."

This is despite the fact that female designers bring a unique perspective to the table, according to Toogood, and can sometimes even be better at capturing that elusive emotional quality that helps an object resonate with people.

"The industrial designers have realised sales are showing that it pays when you create something that connects with other human beings," Toogood said. "We don't need more chairs, more rugs. So how can you make something that's actually going to connect with people?

"It has to hold something other than the rigour of design and proportion and perfection of material, it has to have something else," she added. "What's that magic ingredient that connects people to that object? That's what I'm really trying to discover."

"I achieve it on some things and I don't on others, and I don't always know why."

Other highlights from this year's edition of Milan design week include an inflatable gaming chair from IKEA and lighting sculptures by Leo Maher that reference "queer legends".

Rude Arts Club is on display at the CC-Tapis showroom from 16 to 21 April. See our Milan design week 2024 guide on Dezeen Events Guide for information about the many other exhibitions, installations and talks taking place throughout the week.