A photo widely shared on social media apparently shows Stokes walking through Heathrow Airport with large equipment bags.
By being in Christchurch, though, Stokes is only a comparatively short flight away from Australia and could quickly join the England team if police in Britain decides not to press charges after investigating his involvement in an incident outside a nightclub last September.
The England and Wales Cricket Board (ECB) said the former worldwide was making a private trip to spend time with his family, but Canterbury have confirmed that they've entered into informal negotiations with the 26-year-old.
In the fallout from the first Test loss, England all-rounder Ben Stokes has boarded a plane from the UK.
He was arrested before being released without charge and police and the European Central Bank are both still investigating the incident.
Ashes 2017: Ben Stokes on way to New Zealand and in talks with Canterbury after 'England call-up' frenzy
Stokes moved to England with his parents as a 12-year-old after his New Zealand rugby league worldwide father, Ged, took up a coaching job in Cumbria. "His travel arrangements have not been arranged by the European Central Bank", a statement read.
"He is not on his way to the Ashes, England Lions or any other official training camps with the English setup".
Canterbury meet Otago in a 50-over match on Sunday.
"But until then, we are unable to provide any more detail on the status of the deliberations".
Stokes has not been ruled out of the five-test series, but the England and Wales Cricket Board will not consider him for selection until further notice as it awaits developments in the ongoing investigation.More news: Thamel: Dan Mullen targeted to be next head coach at Florida