Nelson pleaded guilty to two offences of “harassment without violence” as the judge heard how he sent “abusive and unpleasant” emails to Ms Berger in March, before leaving similarly abusive telephone messages for Ms Smeeth two months later.
These were intercepted by Ms Smeeth’s assistant Cathy Perry.
The JC understands that Nelson also made a series of threatening phone calls to the consituency offices of both MPs.
Nelson's lawyer, who refused to give her name to journalists in court, said her client was angry about the debate over antisemitism in Mr Corbyn's Labour, adding: "He felt rightly or wrongly that the two MPs were trying to destabilise the Labour Party and Jeremy Corbyn's leadership."
A Labour spokesperson told the JC that Mr Nelson was currently not a member of the party.
In March, MP Wes Streeting, who has been vocal in the fight against Labour antisemitism, received an abusive email from Nelson, in which he wrote: "Resign, go f**k yourself or better yet kill yourself you worthless Tory."
