Asked on Sunday morning about the initial clip and police statement, Education Secretary Bridget Phillipson said: “The police are now investigating the matter.
“I think that it’s important they’re allowed to get on and do their job and there’s not much more I can say at this point.”
Former Conservative MP Dehenna Davison, whose father died from a single punch, called the CCTV footage “horrendous”.
In a post on X, external, she said: “The police are investigating and I am sure the full facts will emerge soon.
“I have spent years working with One Punch UK to raise awareness of the dangers a single punch can cause.
“Such violence – whatever the background to the altercation – is never and should never be justified.”
Amesbury has been a Labour MP in Cheshire since 2017 and served as a shadow minister between 2018 and 2024.
In the July general election he won his constituency with a majority of 14,696.
In July 2023, a 56-year-old man was found guilty of stalking and harassing Amesbury at his constituency office and in town.