There are a number of considerations to take into account when looking at whether you can rely on this right.
If you do not have a right to do this under the terms of your contract with the employee, then to do so may well be an unlawful deduction from wages (which is a straightforward claim for an employee to bring and is often difficult to defend). You mention that this right is set out in the disciplinary rules. To be effective for this purpose, those rules would need to be properly incorporated into the employee’s contract (which generally handbooks should not be but sometimes parts of them, like disciplinary rules, are). This right must be set out very clearly. The position may be different for staff that do not have guaranteed hours and do not have a right to be paid if they are not working – this may include casual staff.
Even if you do have this right there are other issues to consider. You need to be careful not to unlawfully discriminate in exercising this right. If someone is late due to childcare responsibilities, to not pay them (and/or to discipline them) may be discriminatory. Similarly, you need to think about disability discrimination if someone cannot get into work on time because of their disability. You mention that this applies mainly to part-time staff. This could be problematic as part-time staff have certain protection against less favourable treatment.
You will also probably need to follow a fair procedure before you decide to not pay the employee. If this is a disciplinary penalty (which it probably would be particularly as the right is contained in the disciplinary rules) then you should observe the ACAS Code of Practice. If you do not then the employee could receive an uplift of up to 25% in some types of compensation (including for unlawful deduction from wages and, if it leads to a dismissal, for unfair dismissal).
One possible alternative to the deduction in pay is to treat it as a disciplinary issue (and give warnings to improve etc). You would need then to follow a fair procedure taking into account, for example, the ACAS Code of Practice.