After cancelling, you'll continue to be able to watch BritBox until your current billing cycle ends.
Example: If you're subscribed on a monthly plan, and your plan renews on the 15th of the month, if you cancel on the 7th of the month, you'll continue to be able to watch until the 15th.
You'll need to cancel at least 24 hours before your plan is due to renew.
You can find your renewal date, and make changes such as cancellation in your BritBox account.