OK bit confused here - this sounds a bit suspect! DO NOT send anything with your normal signature on.
You can write back, but DO NOT USE your normal signature, or sign over a date or row of 'x's etc. The idea is that they cannot get your true signature copied and pasted onto another document. If as they say they do not hold your signature on record how can they know what you send isn't your proper signature?
In order for a credit agreement to be valid it must have your true signature on a compliant document. That is not to say that they must send a copy of this signed and compliant document in response to a s.78(1) request - they can send an unsigned copy of a document identical to the one you would have signed at the time.
Normally if a creditor has a signed agreement they will send it in order to avoid lengthy and expensive correspondence. If they don't have one they tend to wriggle with obtuse, confusing and often threatening letters.
It sounds as if they don't have a signed and executed agreement, but I would recommend you do a Subject Access Request to the Data Controller of each of the CCCs. There are plenty template letters around the net. This should bring back a signed agreement if it exists (but again is not guaranteed - these CCCs are slippery suckers).
You need to do some more background reading around this forum. Check out anything posted by Stubie and conmankiller (and others). Also get a copy of the Consumer Credit Act and its associated Consumer Credit (Agreements) Regulations.