Yes, they can
If you are 'always late' they are not trying to make you work a different shift, they want you to work the hours set out for you when you were employed.
However, are they saying you must not be late or lose your job?
With whom did you have the agreement to come in 30 mins late everyday?
The age of your children will also be relevant to you. Do you have any under 7?
http://www.direct.gov...Dismissal/DG_10026696
School opens at 7? That's very early, even for a school with a breakfast club
Are you UK based?
This is a UK web site and primarily answers will be for UK law