On-one was founded nine years by Richards, a former journalist for MBUK and other MTB titles, and Dave Loughran of Planet X.
Richards designed the bikes - including a number of iconic singlespeed models - from his shed in Todmorden, Lancashire.
Loughran said: "On-one is a direct selling single speed and mountain bike brand offering incredible value and products that major manufacturers wouldn't consider viable, or simply wouldn't understand."
With Richards leaving the company, Planet X is searching for a new designer.
"We are looking for a new designer and the opportunities are out there to continue to fill a niche that big manufactures can't see. We always said that our most successful projects were finding the 'niche of a niche' and that's a tradition were going to continue," said Loughran.
"I believe a new designer, with different ideas and a fresh look will help take On-one further along its unusual path. I am sorry that Brant is leaving and wish him every success. He has been an influential part of the team that has built a brand with strong foundations and a cult following."
Richards is to create a bike and accessories brand for mail-order retailer Chain Reaction Cycles.
"I'm spending the next couple of months either in my shed, or in Taiwan, working hard to get a lovely range of frames and components, for launch under a new brand name in early May. What I'm trying to achieve is that fast route to market, volume purchasing, great margins, all in key areas that the big brands aren't hitting.
"And if that fails, I've got a backup plan of going to sell odd hats and beef jerky."