The statutory disciplinary procedure applies to suspensions without pay, even where these are to investigate misconduct rather than as a sanction for it. An employer should issue a Step 1 letter setting out why it is contemplating suspending an employee without pay prior to taking that action, so that the employee has a chance to argue against the suspension before it starts.
There is no obligation to hold a meeting to discuss the decision to suspend, but the employee could presumably appeal it under Step 3 of the statutory procedure. The procedure would then have to be followed afresh should the outcome of the investigation lead the employer to consider further disciplinary action. (Wilf Gilbert v Bunn, EAT)
Failure to do this may only be important if there is no contractual right to suspend without pay, so that the employee has a deduction from wages/breach of contract claim. Compensation for this claim could then be increased by up to 50%.
There is also a (questionable) obiter suggestion in a recent case that, if a one-off investigatory suspension without pay is the prelude to dismissal arising out of the same conduct, a failure to follow the procedure for the unpaid suspension could render the dismissal automatically unfair and lead to a potential 50% uplift to dismissal compensation.
Paid suspensions are expressly excluded from the statutory procedure, but it is still best practice to confirm the suspension in writing.