The Wellingtonian died following an 11-bike pileup during a Supersport race at Oulton Park which also claimed the life of English rider Owen Jenner.
Another New Zealand rider Morgan McLaren-Wood was also involved in the crash and was treated for minor injuries.
Richardson, from Wainuiomata, who was 29, had been based in Britain since 2019.
He was a previous New Zealand rider of the year.
Richardson competed for the Astro-JJR Hippo Suzuki team and finished ninth in last year's British Supersport Championship.
A British Superbike statement said: "Exiting turn one, Old Hall corner on the first lap, there was a chain reaction incident involving 11 riders falling. The race was immediately stopped and trackside medical services deployed.
"Due to the extreme severity of the incident and ongoing medical intervention, the remainder of the Bennetts British Superbike Championship event was cancelled.
"This catastrophic accident has tragically resulted in two riders being fatally injured, and another sustaining significant injuries."
The statement said Richardson was initially treated trackside, then taken to the circuit medical centre before being transferred to Royal Stoke University Hospital with severe chest injuries. He died prior to arrival.
The other rider, Owen Jenner, who was 21, was initially treated trackside and then taken to the circuit medical centre, where despite further resuscitation treatment, he died from a catastrophic head injury.
British rider Tom Tunstall suffered back and abdominal injuries and a further five riders, including McLaren-Wood, were transferred to the circuit medical centre with minor injuries, which did not require transfer to hospital.
Three further riders were also involved but were uninjured.
The Motorcycle Circuit Racing Control Board and MotorSport Vision Racing are investigating the incident in conjunction with the Coroner and Cheshire Constabulary.
