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"We'll work our way up, if people like us, to bigger venues," Prince said.
His first stop was the East London home of British soul singer Lianne La Havas, who met Prince last year while she was touring the United States. The pair bonded over common musical tastes and a shared love of tea.
In her cozy living room in front of a crackling fire, the band played two acoustic tracks of what Prince called their "funky rock `n' roll," or "funk `n' roll," including the newly released single "PretzelBodyLogic."
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Later, Prince and the band showed off its funk-laced, punk-edged sound in an unannounced late-night set at the Electric Ballroom, a landmark venue in north London's music heartland of Camden. He said he'd be back at the club on Wednesday - "a lot earlier and a lot funkier."
The trip to London, he said, is "open-ended."
"We're going to be here until people don't want to hear us anymore."
The tracks on the new album were developed during epic jam sessions at Prince's Paisley Park studios near Minneapolis.
"We've been together for over a year and it's perfect," said Prince, who sipped a mug of strong tea with honey as he chatted to La Havas, her housemates and three journalists in the British singer's brick Victorian house. "The more we play, the more fun it is, and addictive it is."
Drummer Hannah Ford said the band sometimes jammed for 12 hours or more in days and nights of music interspersed with games of ping pong.
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"That's our amazing life," she said. "And we wouldn't want it any other way. We are literally living a musician's fairy tale, and it is now our reality.
"Once you start jamming you sort of forget about the time," she said of the band's sessions with Prince.
"A lot of the time we didn't even know we were recording for an album. We were just jamming and vibing off one another."
Prince, she said, is "an incredible teacher in all the genres - rock, punk ..."
"And ping pong," added Prince.
For 55-year-old Prince - a genre-bending musical pioneer and outrider for more than three decades - the unusual promotional tour reflects a determination to do things his own way.
"I was in it (the music industry) and got out for obvious reasons," he said. "I'm just hooking up with like minds."
He said he's sworn off contracts and deadlines because "it's just no way to make art."
Prince said he hoped to record the band live during their stay in London, as well as buying "some clothes - and some tea."
Asked if - as rumored - he would play the Glastonbury Festival in June, he didn't issue a denial, but said he was trying to "slow time down" and live in the moment. "I can't think of the festival now."
He spoke about his decision to launch a lawsuit - later dropped - against fans who posted links online to unauthorized footage of his performances.
"Nobody sues fans," he said. "It's just a poor way to phrase it. A bootlegger is a bootlegger, a scalper is a scalper. They know what time it is.
"Just sharing music with each other - that's cool," he said. "It's the selling that becomes the problem."
He claimed not to have noticed that 2014 marks the 30th anniversary of the release of his groundbreaking album "Purple Rain," regularly hailed as one of the best records of the 1980s.
"I don't look back," he said.