It's not your fault; contact your card issuer immediately asking them to start the chargeback procedure, inform them of the situation and the dentists continued failure to respond to any of your numerous attempts to contact them to resolve this matter.
You are covered under S75 whether abroad or at home, as long as the supplier has breached their contract to supply the goods or services....which they have, also further failing to communicate with any open intention to remedy or reimburse you for their failures.
Mod - For the avoidance of confusion, posts have been edited at the request of both contributors due to a change of details made in the original post.