Sir James has threatened to challenge both Labour and Conservative MPs who fail to support a referendum on Britain's membership of the EU - although so far it is the Tories who have felt the heat most.
Mr Shore, Labour's most senior Euro-sceptic, is standing down at the election, but his support for a rival political party will irritate the Labour leaders and is a breach of party rules.
Last week a 78-strong Tory rebellion in the Commons over Sir James's demand for a "full" referendum was overshadowed by a furore about his financial support for one rebel leader, MP Bill Cash. Mr Cash was forced to renounce future contributions from Goldsmith funds.
Sir James launches an attempt to woo Labour's Euro-sceptics today, which could spell trouble for the Labour leader, Tony Blair, of the kind which the Prime Minister, John Major, has suffered at the hands of a man who has declared his willingness to spend as much as pounds 20m promoting his views in the run-up to the election.
Sir James has given a strategically-timed interview to the left-wing, Euro-sceptic Tribune newspaper today.
In it he says that although he is not in favour of Britain pulling out of the EU, he thinks that Britain should try to "split Europe" in order to block a "federal state".
Withdrawal "would be a bad thing for Britain" because it would then be "an island off a German-unified continent", he said.
However, Britain should "insist on a Europe of nations and go in there and fight for it. It has to either convert or split Europe".
Sir James insisted in the interview that his single-issue Referendum Party "is neither of the left nor the right. It simply exists for that stated purpose. And if the left is interested in some of my ideas, that is all well and good."
Mr Shore, who is chairman of the Labour Euro-Safeguards Campaign, said: "It is very important that the British people should have a referendum, and the influence of the Referendum Party is the pressure they are putting on the political parties."
Of his implied support for candidates other than official Labour candidates, Mr Shore said: "I'm not recommending such people, but I think that it is a very good idea that the people of this country have a referendum."
Sir James's Referendum Party, which demands a referendum on more than just a single European currency, has taken a series of full-page newspaper advertisements recently, has employed a polling company to carry out opinion research and is planning a full-scale party conference in Brighton in October.
When asked if Sir James had funded the Labour Euro-Safeguards Campaign,and if he might offer financial support to Labour Euro-sceptics, his spokesman said: "We do not consider this a sectarian matter and would be willing to support all mainstream organisations which are in favour of a full referendum."
However, Mr Shore said that the Euro-Safeguards Campaign had "emphatically not" been offered or accepted any funds from Sir James, and nor would it.Reuse content