The expenses scandal dominated newspapers' front pages for weeks, as it emerged that many members had claimed a variety of expenses, including toilet paper, a shelter for ducks and the cost of cleaning a moat.
The ruling Labour Party has barred Morley, a former minister, Chaytor and Devine from running for new terms in the upcoming election.
White has resigned as the Conservative Party's business spokesman in the upper chamber and been suspended as a member of the party's group in the assembly.
The lawyer representing Morley, Chaytor and Devine argued before the court that parliamentary privilege should prevent them from having to face a criminal trial.
Julian Knowles said: "They maintain that to prosecute them in the criminal courts for their parliamentary activities would infringe the principle of the separation of powers, which is one of the principles which underpins the UK's constitutional structure."
After a brief appearance at the court, a short distance from parliament, all four men were released on unconditional bail and ordered to appear before a higher court on March 30.
Britain is expected to hold a general election on May 6 and the latest polls show the result could be inconclusive, with neither of the two main parties winning an outright majority.
The expenses scandal makes the election outcome even harder to call, with smaller fringe parties and independent candidates expected to pick up votes from disgruntled Britons.
The four men face a maximum sentence of seven years in jail if convicted.