As you paid by card, raising a chargeback claim, based on your dispute with the clinic, to have the payment transaction reversed, could be the "quickest" option, but there is the risk that your claim could be late, having regard to the date of the payment.
If you are objected that the chargeback claim was raised late, you should emphasise that the issues with the clinic surfaced after their cancellation of the appointment, which happened only in January, therefore the deadline for the claim should not run from the date of the payment transaction (please note that there is no certainty that the bank/card provider will accept this).
In addition to that, you should formally complain to the clinic, or, if you have already done it and your complaint was rejected, you should escalate it to an association of which they are members or to the Parliamentary and Health Service Ombudsman where applicable (https://www.ombudsman.org.uk/).
In the complaint, you should emphasise that you had to cancel because the clinic cancelled multiple appointments and, after that, you found the negative reviews on TrustPilot.
I hope this information is helpful and I wish you the best.
Please do not hesitate to contact JA again if you need help and you may ask to speak with me directly if you wish.