You may be able to challenge this on grounds of disability discrimination, but it will depend on the reasons given by the employer for withdrawing the job offer.
You would need to be able to show that the employer has changed their mind because you have a mental health problem, and not because they believe the information in the DBS certificate suggests that you pose a risk to children or vulnerable adults.
If you think you may have been discriminated against in this way, you should get advice from an employment law solicitor.
For more information on disability discrimination by a prospective employer, and how you can complain about this, see our information on discrimination at work.
This information was published in February 2017. We will revise it in 2019.