Clarkson’s Top Gear contract has not been renewed by the BBC after an internal investigation found he attacked show producer Oisin Tymon after an angry — and lengthy tirade — in a hotel in the county.
Returning to his home shortly after 3.30pm, Clarkson refused to answer when asked if he was worried about being arrested.
Instead, he said: “All I would like to say is ... I wish people would leave Ois alone because none of this was his fault.”
Jeremy Clarkson could face police action over attack
In a statement, the force said they had been contacted by “concerned members of the public” asking what action they were taking.
They said: “No one who was present at the hotel during the incident came forward to report an offence to the police. Nonetheless, we have a duty to investigate where we believe an offence might have been committed, and that is what we have been doing with this case.
“We have already spoken to some people who were in the hotel at the time, but there are still others we need to speak to, who could help us to determine exactly what happened.
“Also, as is usual in these circumstances, we have made contact with Mr Tymon through his lawyers, to ask him to speak to us so we can ascertain how he wishes to pursue this matter.
“When these routine inquiries are completed, we will be able to assess whether or not further action needs to be taken from a police perspective.
“Meanwhile, we’d like to reassure the public that the matter is in hand, and we are dealing with it responsibly and proportionately.”
'Leave Oisin alone…None of this is his fault': Clarkson
Clarkson faces an uncertain future as reports suggest the former Top Gear host’s co-stars may leave the show alongside him.
BBC director-general Tony Hall has made it clear he wants the programme to continue, but co-host James May said he was considering his position, and Richard Hammond declared it the “end to an era”.
The BBC confirmed that Clarkson’s contract would not be renewed after its investigation found the presenter’s attack on Mr Tymon left him needing hospital treatment.
As for the 54-year-old’s broadcasting future, two major companies — Sky and Channel 4 — are understood to have ruled out working with him, while ITV would not comment on “a BBC issue”.
However, the BBC’s creative director, Alan Yentob, offered a potential olive branch by refusing to rule out a return to the corporation for Clarkson in the future. He told BBC2’s Newsnight: “Of course I wouldn’t rule that out, but that’s not for now.”
All three presenters’ contracts run out at the end of this month.
Read more stories from around the world here