What you said
Get the senior leadership team to man all entrances to school and "book" those who arrive late with a lunchtime detention that day. A second late arrival in a fortnight or a month and the pupil gets an after-school detention of 20 minutes. Another, and it's a 30 minutes after school, then 40 minutes etc.
Follow up each instance of lateness by contacting parents. Find out why they are late. You may unearth lots of pastoral issues and be able to bring parents onside. Punishment: minutes late equals minutes' detention.
The expert view
The best way to ensure a system works is by making it as streamlined and simple as possible. Parents are involved in lateness, but there are factors behind the scenes that we don't see, so beware making snap judgements.
I wouldn't bother with complicated sanctions - "Three minutes late, so three minutes' detention" (who cares about a three-minute detention?). If a child is late, give them half an hour's detention (or more, but a flat tariff) that day. If they don't show up, escalate the sanction - and make sure the person administering the detentions is a bit of a "hardass". Get them doing work in the session - not homework, or the sanction becomes an opportunity. Something dull.
If they don't attend the detention, someone should call their parents that day and ask why. Then the parents could be called in pronto, and the child would get a shock.
In almost all cases this will work, with some repetition, as parents don't want to be called in every week.
Tom Bennett is author of The Behaviour Guru and Not Quite a Teacher. Read more from Tom on his blog, behaviourguru.blogspot.com, or follow him on Twitter at @tombennett71. His latest book, Teacher, is out now, published by Continuum. Post your questions at www.tes.co.ukbehaviour.