Jamie Hewlett is taking a couple of years off. The artist, who was one half of Gorillaz, is turning down almost every offer of work to concentrate on his own projects.

After a decade of working on Gorillaz, without "a free week to contemplate anything else", he's enjoying the space. "I got tired of all the stuff I had been doing – working on computers and doing animation and the endless conveyor belt of drawings required for a project like the Gorillaz," he says.

His exhaustion with the musical-visual project is timely. Damon Albarn, his collaborator, announced last week that the project was unlikely to continue. He said had fallen out with Hewlett, explaining the pair were "at cross purposes somewhat" on their last record, released in 2011, and while not being on friendly terms "sounds very juvenile", he said, "It happens. It's a shame."

Hewlett is more sanguine about the split. He believes that while Gorillaz has "run its course for now, it doesn't mean it's packed away for good", though if the two collaborate again he would like it to be on something "completely different". There are projects that they worked on between Gorillaz albums which never saw the light of day that he thinks could be dusted off in the future.

As for his relationship with Albarn, he thinks it's natural to spend time apart. "We've lived in each other's pockets for the last 13 years: we shared an apartment, our kids have grown up together, we've been inseparable for a long time, and sometimes it's good to have a break," he says. "We haven't fallen out, I just want to do some of my own stuff, and Damon has many projects – he's always doing 10 things at once – so it's all right to separate for a bit and try different things." But he's adamant he likes working with Albarn, that, when they collaborate, "the ideas come thick and fast, and it's an enjoyable process".

Hewlett was first introduced to Albarn as Blur's first album was released, as his former partner Jane Olliver, originally a member of Elastica, was friends with – and formerly girlfriend of – Blur's lead guitarist, Graham Coxon. But it was not friendship at first sight with Albarn. "He didn't like me at all, and I didn't like him. We spent 10 years, every time we saw each other being a bit rude to each other, not talking to each other," he remembers. He claims to have never understood why, putting it down to similarities that can cause a clash. Others have speculated it was due to friction over Olliver, previously Coxon's girlfriend, before her relationship and two children with Hewlett. But after a decade of mutual mistrust, something changed. "One day, we suddenly clicked, became very good friends, it was the complete reverse. So, yeah, strange," he remembers.

In contrast with his manic work schedule of the past decade, Hewlett is relaxing in the Normandy sunshine when we chat. Even his voice is laid-back, in time with the pace of rural French life. He is writing a story, though declines to share details as he expects it to take a long time to come to fruition, and teaching himself to paint in oils. "It's wonderful, like learning to draw from scratch all over again – I've been painting lots of really terrible pictures, but they're slowly getting better." So far, he is unsure whether it is for personal pleasure, or whether, in a couple of years, there may be enough work he is proud of that he would like to exhibit.

France is now his part-time home, and he's learning the language. "I'm 44, my brain is a bit like a dried-out sponge. I understand most of what people say now," he says. Last year, he married Emma de Caunes, a presenter on the French music programme La Musicale, who also played Zoé in The Science of Sleep. They met while she was researching Gorillaz, and it was, he says, "love at first sight". They now live in Bastille with de Caune's nine-year-old daughter, while Hewlett returns to London most weekends to see his "grown-up" children, aged 16 and 12. He raised them on a diet of Studio Ghibli films, ignoring Disney. "Most animated kids films nowadays are pretty awful," he says. Now his elder son introduces him to new music.

One recent job Hewlett did not decline was designing special edition Absolut vodka bottles – in supermarkets now – following Andy Warhol, David Shrigley and Damien Hirst, who have also made their mark on the spirit. He created characters epitomising high points of London fashion, taking in the 18th-century and a Dickensian dandy, a pinstriped gent, Sixties chick, punk, ska and 1980s casual. An accompanying game will be launched through Facebook. "I identify with the ska guy – I tried to adopt the look myself but my parents wouldn't buy me the necessary clobber," he says. He remembers his teenage years with relief that they are over. "I grew up doubting myself. It was a very spotty, frustrating, worrying time."

He went to art college, before being rejected from Kingston Polytechnic by an interviewer who thought graphic art inferior to other genres. He thinks snobbery towards graphic art remains strong. "Some comic artists I've known are better than most contemporary artists with work hanging in Tate Modern. But then, there are a lot of crappy artists around now." He thinks it's easy to fake – "the market is flooded with charlatans" – and while he admires the stencil artist Banksy, he finds the "army of copiers" in his wake "ridiculous". "And they're all considered legitimate artists," he says, baffled.

Hewlett took a job on a computer magazine, drawing one illustration a month for £50, inspired by artists including Ronald Searle, who died last December, and Chuck Jones, creator of Daffy Duck and Wile E Coyote. His work proved popular, and he created the counter-culture Tank Girl comic strips for the now-defunct magazine Deadline. The comic strips were so popular they were published internationally, and Tank Girl caught the eye of Hollywood. Hewlett, then 22, was dazzled by movie-machine star treatment, and agreed to a feature film starring Lori Petty in the lead role. But he disliked the end result; a feeling shared by cinema audiences. "Hollywood buys into this cool character, but ultimately didn't want to do it the way I wanted," he says. "I wasn't aware until too late I was losing control."

The experience was so unsatisfying that while directing a film is one of Hewlett's ambitions, he's hesitant to see work diluted into disappointment. "I need to find a way of retaining creative control," he says. That wariness led to Hewlett and Albarn meeting three major Hollywood studios in Gorillaz's heyday, and writing two scripts, yet pulling out when studios said their vision was too dark.

Instead the pair made Monkey: Journey to the West, in 2006, which played at the Royal Opera House and is the project of which Hewlett is most proud. "I never intended to do stage designs or design costumes, but I really enjoyed it," he says.

Equally, he never intended to direct videos, as he did with Gorillaz. But, while drawing is his speciality, he says he has no fear of exploring different media to bring ideas to life. "I'm always having ideas," he says. "I'd like to continue being able to realise the ideas I have."

His time off, working on his own projects, marks a new chapter. "I'm not bothered about doing something as successful as Gorillaz because I doubt that will happen. I want to do stuff that excites me and is enjoyable," he says. At the moment he is enjoying writing. "I'm lost in my own little world, but eventually it will have to be shaped."