It depends on your written contract of employment. This is a deduction from your pay (the 30 minutes of work minus the few minutes that you did not work).
It is against the law to make a deduction from wages unless either:
the worker has given their prior written consent to the deduction.
Your employer can only make this deduction if there is a clear rule in your contract of employment, or in a staff handbook or policy incorporated into your contract, allowing your pay to be cut for this reason.
Even if there is a term in your contract allowing your employer to behave like this, if cutting your pay by half an hour means that your average basic hourly pay during your pay reference period falls below the National Minimum Wage, your employer is likely to be breaking minimum wage law.
Your pay reference period is based on the pay arrangements where you work. It will be a day if you are paid daily, a week if you are paid weekly and a month if you are paid monthly.
If the rule impacts disproportionately on a particular group of workers, such as women with caring responsibilities, you might be able to argue that it is indirectly discriminatory.
Also, this sort of punitive rule is likely to impact on specific workers, such as pregnant workers who struggle with their commute, physically disabled workers, or carers with a tricky school drop off and creates a risk of direct discrimination and harassment.
Your employer is also likely to lose workers’ goodwill, which could impact negatively on productivity, especially if no allowance is made for circumstances beyond the worker's control, such as bad weather or traffic disruption.
If a union is recognised at your workplace, ask your rep to raise these issues with management. If there is no union recognised but more than one worker is affected, consider organising together and raising a collective grievance. Also, think about organising to grow the levels of union membership where you work, so that an application for union recognition can be made. Individual unions provide help and guidance on the best way to do this.