Any appeal would be heard on June 29 before the Lord Chief Justice, a spokeswoman for the Judicial Communications Office said.
Mr Justice Saunders rejected arguments by David Chaytor, Elliot Morley, Jim Devine and Lord Hanningfield that they were protected by parliamentary privilege and should be dealt with by Parliament alone.
"I can see no logical, practical or moral justification for a claim for expenses being covered by privilege; and I can see no legal justification for it either," he said.
His decision "clears the way for what most people accused of criminal behaviour would wish for: a fair trial before an impartial jury", he said.
All four men, who were excused from attending today's hour-long hearing at Southwark Crown Court in central London, deny theft by false accounting. They were each granted leave to appeal.
The defendants' argument - that submitting an expenses form was part of the proceedings of Parliament, and therefore protected by parliamentary privilege - was akin to saying that the coin used in a slot machine was part of its machinery, Mr Justice Saunders said.
"The decision that I have had to make has not been easy," he said.
"Very important constitutional principles are involved which must be respected, and that must be the case even if it leads to a result which is unpopular not only with the public but also with Members of Parliament."
He went on: "The principle that all men are equal before the law is an important one and should be observed unless there is good reason why it should not apply.
"To do otherwise would risk bringing both the courts and Parliament into disrepute and diminish confidence in the criminal justice system."
The judge added that it was preferable for "criminal allegations to be decided by criminal courts who are equipped to deal with them".
He accepted that the processing of the expenses forms was part of the workings of Parliament, but added: "I see no reason to extend that privilege to cover the submission of the form.
"There has to be a line drawn and it has to be drawn somewhere."
Claiming expenses was for the benefit of the individual, rather than for Parliament as a whole, and no member could be criticised for failing to carry out his duties as an MP if he did not claim the allowances, he said.
"None of the justifications for the existence of privilege would seem to apply to the submission of the form," he said.
"In my judgment, it does not come within the scope of the 'exclusive jurisdiction of Parliament' on any sensible construction of that privilege."
While it was accepted that privilege extended to "incidental matters" such as drafts of speeches, it would be "stretching the meaning of the word 'incidental' beyond its ordinary meaning" to say that it also included submitting expenses forms, he said.
The judge added that he would have raised the question of parliamentary privilege himself if the defendants had not raised it first.
The privilege was that of Parliament, and not of any individual member, so the defendants would not have been able to waive it even if they had wanted to, he said.
"Comments in the media and from prominent politicians to the effect that they could were misconceived," he said.
"It follows that the even more extreme suggestion in some quarters that the fact that the defendants have raised this issue is some indication of guilt is not only misconceived but also unfair."
Former Bury North MP Chaytor, 60, of Todmorden, Lancashire, is accused of falsely claiming rent on a London flat he owned, falsely filing invoices for IT work and renting a property from his mother, against regulations.
Former Scunthorpe MP Morley, 57, of Winterton, North Lincolnshire, is charged with falsely claiming £30,428 in interest payments between 2004 and 2007 towards a mortgage on his home which he had already paid off.
Former Livingston MP Devine, 57, of Bathgate, West Lothian, is accused of wrongly submitting two invoices worth a total of £5,505 for services provided by Armstrong Printing Limited.
He also faces a second charge alleging that he dishonestly claimed cleaning and maintenance costs of £3,240 by submitting false invoices from Tom O'Donnell Hygiene and Cleaning Services.
And former Essex County Council leader Lord Hanningfield, who is also known as Paul White, 69, of West Hanningfield, near Chelmsford, Essex, faces six charges of making dishonest claims for travelling allowances.
Each of the four defendants, who are all on unconditional bail, will now face a separate criminal trial, pending the outcome of any appeal.
