Unless the supplier has provided you with the 11 point information prior to the conclusion of contract contained within the Prior Information in the link below (particularly point 6, the existence of a right to cancel), then under the distance selling regulations the contract is legally unenforceable and a refund is due.

http://www.out-law.com/page-430#Prior

Can a deposit be refunded outside the cooling off period, if it was paid over the phone but the dealer only sent an invoice, with no details about how to cancel as specified by the Distance Selling Regulations ?

No paperwork signed, payment taken from a credit card.