He was speaking after an incident in Parliament on Thursday left Ukip MEP Steven Woolfe in hospital after an alleged punch up with a colleague and in the wake of Diane James' decision to stand down from her role, just 18 days after she was elected party leader.
On Friday, Woolfe was said to be making a good recovery and told the Daily Mail that Mike Hookem, a party colleague had thrown a punch at him after a heated meeting in Strasbourg.
James, a 56-year-old MEP for South East England, said she did not have "sufficient authority" to see through changes she had planned.
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Ukip now faces the prospect of a second leadership contest within the space of weeks.
MacShane said, “Ukip has always been a one-man, one-policy show. Once the entertainer-in-chief, Nigel Farage, retired having won his only policy objective - quitting Europe, the show was over. I debated with Diane in the Brexit campaign and Nigel Farage she isn’t.
“It was one of the worst performances from any elected politician I ever heard. Ukip have never one a single seat in the UK Parliament unless via Tory attention-seeking defectors.
“They win a few council seats, often inherited from the BNP after the BNP faded away to be replaced by Ukip as the main vector of xenophobic and anti-Muslim politics in Britain.
“But Ukip has never been more than a single issue party and now that issue has gone away and all their MEPs will be on the dole after May 2019 there is little point in the party existing, let alone fretting about who leads it.”
Roger Helmer, a former Tory MEP who defected to UKIP, also told this website, “ I am sorry to lose her but glad she was prepared to bite the bullet and not to let the situation drag on.”
James, who says she will continue as an MEP, succeeded Nigel Farage on 16 September after he quit in the wake of the UK's vote to leave the EU.
James said in a statement earlier this week that she had decided "for personal and professional reasons" not to take up the helm of the party, but would stay on as an MEP.
"It is with great regret that I announce that I will not be formalising my recent nomination to become the new leader of the party with the Electoral Commission," she said.
"Having won the enthusiastic support of party members, I was nominated by them as the new leader at the recent Ukip Bournemouth conference.
"Since that time, I have been in discussion with party officers about the role. It has become clear that I do not have sufficient authority, nor the full support of all my MEP colleagues and party officers to implement changes I believe necessary and upon which I based my campaign.
"For personal and professional reasons, therefore, I will not take the electoral process further."