Chroma chameleon: The bright essence of Frank Bowling's paintings floods his London home

If you visit Tate Britain, you might find yourself in a single-room exhibition showing a single facet of the artist Frank Bowling's work. This is a "Focus" gallery, and it is filled with the abstract expressionist's "Poured" paintings: gorgeous, colourful, flowing things created in the 1970s by pouring paint on canvasses in multiple layers, letting it slide and stream, pool and puddle.

The show is almost an artistic homecoming for the 76-year-old: he lives just around the corner, in the Pimlico flat he has owned since 1984, with his wife, the textile artist Rachel Scott. The Tate k has long been an important place for Bowling: "In the early years I rather fancied living in this neighbourhood," he explains. "As a younger artist I used to go in almost every day."

Born in Guyana, he moved to the UK in his teens. While serving in the RAF, he met Keith Critchlow, an expert in geometrical patterns. Through him, Bowling became interested in drawing, and began studying at the Royal College of Art, graduating in 1962 with the silver medal (David Hockney nabbed gold).

For most of his career, Bowling divided his time between London and New York. "I had a lot of problems when I was younger, being pigeonholed," he says. "London tended to remember only the fact I was a 'black artist'. I got pretty fed up and turned off by it. It was choking me." Bowling would go on to become the first black Royal Academician, but he was resistant to the 1960s pressure to market his work as "negro art". He'd visited the US, and "met Larry Rivers, and his friend Frank O'Hara, and they said, 'Why are you staying in London? They're killing you. Come and live in New York.' So I went. They set it up that I would live in the Hotel Chelsea – and it was the most jumping place."

The "humming" downtown scene had an explosive impact on Bowling's work, and he began moving towards abstract expressionism, playing with colour, surface, materials. But Bowling had left behind his first wife (Paddy Kitchen, a Royal College member of staff while he was a student) and their sons in the UK. "I had to know what was going on with the kids, so I kept coming back. It was bumpy, but very invigorating."

He may not be dashing back and forth so much these days – his health means he makes it over to the US only for shows – but life has never been busier. There are no fewer than six solo exhibitions of his work this year, and he features in the V&A's British Design 1948-2012 and Tate Britain's Migrations.

"I didn't expect it to wear me out, but it has," he says of all the fanfare. "I didn't expect it would, because I get up and the first thing I want to do is work." Bowling still has a studio space in Elephant and Castle. "I spend two hours in the studio in the morning and sometimes two hours in the afternoon, and my head is going round and round with what I'm trying to do – often I bring stuff home."

Indeed, scattered on the floor of his home are new works, drying. He jokes that he has to be careful not to get paint on the rugs – but Scott good-naturedly insists, "It's part of their history really. They actually have quite a lot of paint on them," even though the rugs are the work of her own two hands.

The pair moved in together in the late-1980s. She was also "an obsessive painter", but when a stairway rug began to wear out, she made a replacement, taking weekend courses on spinning and tapestry weaving, and found her calling.

Scott uses the neutral, natural shades of traditional British wool, but when it comes to making things for her husband, she goes all out with colour. She knitted the stripey cover on his chair, a patchwork of rectangles made up of 52 different colours; it's now 25 years old. Scott also sewed their patchwork bedspread – and some 40 dresses ("I so hate shopping!").

If his wife literally wears her life on her sleeve, Bowling works in quite a different way: his art has always gone in phases. He experiments with a technique, immerses himself in it, then moves on. But have the flurry of recent shows reminded him of ways of working that he might want to revisit?

"Absolutely. An awful lot of what I'm trying to do now is revisit areas that I had raced through." he says. So are his current works "Bowling best ofs"? "I see potential in some of the stuff I did, like with the pours, and especially colour: I'm digging deeper and deeper." Witness his recent works hung over the fireplace, fizzing with crimson, pink and orange, or the candy-coloured pieces the couple stand in front of in his studio. He may slow down as he gets older, but there's no plans to turn down the brightness.

'Recent Small Works' is at Eleven Spitalfields, London E1 (elevenspitalfields.com) to 31 August. Poured Paintings is at Tate Britain, London SW1 (tate.org.uk), to 31 March