Daniel Stanton's response

Unfortunately a verbal contract may be equally binding for this type of transaction. The usual problem is a lack of evidence except one word against another, but the fact you gave your credit card details may be used as evidence that you meant for there to be some kind of relationship.
Any legal obligation that does not set down a definite timescale would usually be interpreted by the Courts as having to be done within a 'reasonable time'. Accordingly, very shortly you should receive a tenancy agreement to sign.
If the agents are members of ARLA (the Association of Residential Letting Agents) then you may be able to speak to someone in that organisation for advice. Otherwise, it's just a case of visiting their office.
You could, if you wanted to expend a lot of effort in moving this forward and nothing is happening for a while, apply to the Land Registry for a copy of the title to the property and find out from that the identity of the Landlord. You may then be able to contact them direct and make them aware of the problems you are having. After all, they will be paying the agent to let the property.
Obviously it's difficult to give a comprehensive answer without a few more facts and for that reason, although I am a solicitor, I cannot assume legal liability for my response, but I hope that the information above gives you a few more options to explore. If you are in any doubt as to your legal position overall, you need to take legal advice from a solicitor in a face-to-face meeting, with any other relevant information to hand.