Can I stop an organisation checking the status of my DBS certificate?

Yes. You should contact them and withdraw your consent for any future checks. If they fail to stop, they are breaking the law by accessing data they were not entitled to see. If they persist, you should contact the Information Commissioner's Office, via the contact details on the ICO website.

If the organisation continued to carry out status checks once you have withdrawn your permission, you could also consider removing the DBS certificate from your account; however, this would also mean other organisations would not be able to carry out a status check on it, and you would not be able to add it again.