Very unlikely you'll get a refund. The third party service you paid for did exactly what you paid them to do, they got you an earlier appointment. It isn't really their fault that, exceptionally, the test centre weren't able to send you for your test. If you have been able to rearrange your test with them, there's really nothing you can do in my opinion. If you didn't get a free test rearrangement from the DVSA, then you should be able to get a refund for your booking fee ONLY.