As you’re self employed and running your own business, you’re required to have provisions in place to dispose of your business waste (such as cardboard, paperwork, etc).
Under the Environmental Protection Act 1990, you’re not permitted to use residential facilities for waste, such as using your bins at home (for household rubbish), public bins, recycling or household waste sites, or even disposing by burning!
Where you incur charges for waste disposal (such as using a private waste management company – for example, some Office Supply stores have a shredding service, and charge per bag), these can be claimed as business expenses as they’re a required part of your business activity.
Keep the receipt for these, and add to your expenses as normal.