Banks also threatened to leave Ukip if Hamilton and Douglas Carswell are allowed to stay in the party and if the party’s national executive committee rules Woolfe cannot run for leader.
Banks’ comments come after Hamilton alleged that leadership-favourite Woolfe tried to pick a fight with a fellow MEP “and came off worst”.
Woolfe is recovering in hospital after he was treated for severe injuries following the altercation.
Hamilton, leader of Ukip in the National Assembly for Wales, was attacked for his “disgraceful” comments, with some calling for him to be removed from his position.
Banks joined in the condemnation of Hamilton, writing on Twitter: “If the Tories want him back I won’t punch him.”
Banks said that Hamilton “attacking” Woolfe was the “final straw”.
Speaking to the BBC after Woolfe was taken to hospital, Hamilton said: “It’s most unfortunate but passions obviously run high.”
Banks said he was “utterly disgusted” by Hamilton’s comments and revealed that he was considering leaving the party.
In a statement, Banks said: “Firstly, I was shocked at the events that unfolded today - it goes without saying that I wish Steven best wishes and hope he recovers soon.
“I am however utterly disgusted to see Neil Hamilton touring the newsrooms this afternoon, spewing his bile before anyone knew if Steven was going to be ok.
“He truly is a creature from the gutter who will do anything to get his mug on our screens.
“Tonight I am calling for the immediate suspension of the NEC. Elections need to be held for both a new leader of the party as well as the NEC.
“People say that Ukip is split down the middle between two camps. This is incorrect.
“The Tory troublemakers and fifth columnists represent a small minority in our party, yet they use any opportunity they can do undermine those working tirelessly to hold the governments feet to the flames. This ends today.
“If Neil Hamilton and Douglas Carswell remain in the party, and the NEC decide that Steven Woolfe can not run for leader, I will be leaving Ukip.
“People have worked too long and too hard to get Ukip to where it is today, but it is clear that we ourselves, are at breaking point.”
Earlier today Hamilton said: “I understand there was an argument between some MEPs and Steven, I think, picked a fight with one of them and came off worst.
“That’s what I have heard second hand and it remains to be seen what the full truth is.
“But I don’t know what his current condition is, it’s obviously a serious matter if he has been carted off to hospital with bleeding on the brain as I understand it.”
He continued: “I was told that he was knocked over, hit his head on a window and I don’t know that he was knocked unconscious but it’s obviously had some repercussions.”
Hamilton added: “(Woolfe) just toppled over and hit his head on a glass window and there must have been quite a wallop I guess to have had the impact that it seems to have had.”
His comments were slammed for lacking “basic respect”.
Sources said Woolfe had a stand-up row with fellow MEP Mike Hookem. Hookem is a former soldier and Ukip’s defence spokesman.
When asked if Hookem was involved in the row, a senior Ukip source told HuffPost UK: “I will not deny [that].”
The source also told HuffPost UK that Woolfe was being treated in hospital in Strasbourg for a “suspected bleed on the brain”.
A subsequent statement released by Woolfe from his hospital bed said:
“The CT scan has shown that there is no blood clot in the brain. At the moment I am feeling brighter, happier, and smiling as ever. As a precaution, I am being kept in overnight awaiting secondary tests to make sure everything in fine.
“I would like everyone to know that the parliamentary staff, the UKIP MEPs with me and hospital staff have been brilliant. Their care has been exceptional. I am sitting up, and said to be looking well.
“The only consequence at the moment is a bit of numbness on the left hand side of my face.”