I didn't say they weren't allowed to carry out two credit checks, but it would be good practice not to, otherwise they know they are risking the money of one of the applicants.
In your situation, they had either started the cc on the other applicant, in which case they shouldn't have started yours until they knew for sure that they wouldn't be letting the property to the other applicant, or they hadn't, in which case they should have waited for the outcome of your cc before starting the other one. Makes most sense that way.
Also, if they say they had started the cc so can't refund, they should be able to provide proof of what exactly they have been charged and, if it doesn't total £55, they are profiting from their practice of carrying out more than one cc at a time.