Also listed was General Sir Mike Jackson - once head of the British Army - and David Petraeus, former US Army commander in Iraq and Afghanistan and now director of the CIA.
Zimmerman had targeted the MP for Corby, Northamptonshire, last year telling her to stop using the social networking site Twitter or face the consequences.
The agoraphobic, who lives in a run-down house in Barnwood, Gloucester, told Mrs Mensch that she faced a "Sophie's Choice" - a reference to a novel in which heroine Sophie has to choose between the life of her son or daughter at a Nazi concentration camp.
Zimmerman was charged with an offence of sending by public communication network an offensive, indecent, obscene, menacing message or matter.
At a hearing at Gloucester Magistrates' Court in April, he was found guilty in his absence, having failed to attend on that occasion, blaming his agoraphobia and depression.
He attended court last month for sentencing but a district judge adjourned the case until today so that a pre-sentence report could be completed.
A Scotland Yard spokeswoman said of this afternoon's scheduled hearing: "Zimmerman did not appear, and a warrant for failing to surrender to bail was issued by the court, for him to be arrested and brought before the court at the earliest opportunity.
"The court declined to pass sentence in his absence."
Zimmerman's email, dated August 22 last year, read: "Subject: You have been HACKED :D.
"Louise Mensch, nee Bagshawe, the slut of Twitter. We are Anonymous and we don't like rude c**** like you and your nouveau riche husband Peter Mensch. You have been hacked!
"We are inside your computer and all your phones, everywhere... and inside your homes.
"So get off Twitter. We see you are still on Twitter. We have sent a camera crew to photograph you and your kids and will post it all over the net, including Twitter. C***face.
"You now have a Sophie's Choice. Which kid is to go? One will, count on it c***. Have a nice day. From all of us at MIT 617-253-1000."
The 40-year-old MP, who has more than 58,000 followers on Twitter, immediately called in the police and arranged security for her family.
Unbowed, she went on to tweet to followers: "Had some morons threaten my children by email. To those who sent it: get stuffed losers."
The offensive email was later traced to the IP address of Zimmerman's home computer.
Zimmerman denied sending it, saying his computer had been hacked.
He told the court at last month's appearance that he had no way of getting to today's sentencing, saying: "I am not physically capable of walking and I have no money. I have no money; I simply cannot afford to eat."
Police officers who went to Zimmerman's house said much of it was inaccessible because of the piles of rubbish.
One officer said that in 18 years she had not come across such squalor and appalling conditions.
