I don't think so, Eddie, though your potential employer might argue otherwise if he can show that there may be children around whilst you are there or something like that. I have had some dealings with this issue since the changes came about and the DB Service are now quite strict in who they will provide checks for.
One of the main changes worth a mention is that it is now the job applicant who has to make the request for the check. However, it is the responsibility of the employer to ensure that a check is necessary under the DBS regulations.
There is plenty of guidance available on the .gov website but of particular interest to you may be this:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/260319/DBS_guide_to_eligibility_v2.2.pdf
Page 2 tells you what to do if you have been asked to obtain a DBS check but are unsure if the position requires it. It is not straightforward as far as schools go, but I think the crucial criterion is that the postholder must be in a position to have "regular contact with children". I read that to imply that a post where the holder may occasionally come into contact with children (as people in many jobs might) is not eligible. I would suggest that an after-hours school cleaner is unlikely to have regular contact and so would not be eligible.
The school, of course, will take a different view and the jobsworths at the local education department will want you checked "just to be on the safe side". However, my recent dealings with this issue suggest that the DB service is far more robust than its predecessors and they may take a different view. I suggest you get in touch with them as the guidance suggests.