Government officials have been accused of using “bully boy tactics” as they desperately try to stop businesses campaigning for Britain to leave the European Union (EU).

With Downing Street becoming increasingly worried with the lacklustre pro-EU campaign, whose official launch received widespread mockery earlier this week, the Prime Minister’s key aides have taken to phoning senior businessmen, begging them to back EU membership.

At the same time they are also asking them to sign a letter backing David Cameron’s renegotiation strategy, even though it is now highly unlikely to include any substantial changes to Britain’s EU membership.

One millionaire Conservative Party donor, who did not wish to be named, told The Sun: “I received a call from No. 10. They want to find people to sign up to a letter attacking the Vote Leave campaign.

“I have always been a strong supporter of the party but am concerned about these bully boy tactics.

“I wish they were spending more effort on getting a good EU deal than trying to scare long-standing Conservative supporters.”

Vote Leave, which has been dubbed the Westminster Establishment Anti-EU campaign, has lost two millionaire backers recently after Pimlico Plumbers founder Charlie Mullins and Lord Harris of Peckham quit.

They had both originally signed up to the group when it was known as ‘Business for Britain’, campaigning to support David Cameron’s attempts at renegotiating Britain’s EU membership.

The news comes after Lloyds chairman Norman Blackwell said that without substantial change there was no “compelling economic argument” for Britain to remain in the European Union.

Addressing the House of Lords, Mr Blackwell said: “I do not agree that remaining in the European Union without a significant change in the current treaty arrangements is ultimately sustainable from a political and constitutional perspective.

“Nor do I believe that there is a compelling economic argument to override those considerations.”

Prime Minister David Cameron is expected to finally unveil his renegotiation demands “at the start of November”. The delay has been a source of frustration for many, leaving uncertainty as to exactly what the Prime Minister wants from Europe.

Mr Cameron told reporters on Thursday: “The pace will now quicken and I will be again setting out the four vital areas where we need change, laying down what those changes will be at the start of November.

“So we quicken the pace and quicken those negotiations in the run-up to the December council.”