What are my options? HR withheld details for several weeks required by a new employer (clawback for training) and the new employer has since withdrawn their offer having filled the role whilst I waited for HR.

Expressing anger to or suing either of those employers is a bad idea. You may be correct that requesting and receiving reimbursement for expensive training you received shouldn’t be a reason for HR not confirming dates of employment.

Expressing anger to or suing either of those employers is a bad idea. You may be correct that requesting and receiving reimbursement for expensive training you received shouldn’t be a reason for HR not confirming dates of employment.

And the job market is competitive. Your potential employer had a hiring deadline. Without timely confirmation from your former employer, there was no evidence that you were suitable so they hired their next best applicant. There's nothing you can do about either situation that wouldn’t damage your career as a professional.

For the future, if you intend to include that job on your resume, you can ask a former supervisor to give you a reference letter including their contact info. You can give that letter to potential employers as a contact to confirm employment. For now, the only thing you can do is move on.