The EASA CofA only signifies the certification basis of the aircraft. For most light aircraft this is normal and/or utility. It does not state what an aircraft can be used for. If you want to fly aerial or public transport you comply with the additional requirements of the ANO, i.e. first aid kit, etc. I understand that there should be a new ANO out later this summer which will make these additional requirements easier to find.
At this time if you are operating the aircraft privately you continue as before. Although you have an EASA CofA, the other EASA maintenance requirements are not being implemented by the CAA until the last dates in 2007/2008.
The EASA list of allowed pilot maintenance is a lot larger than the current CAA list. Unfortunately, the EASA requirements state that you must be competent to do the job! This could be interesting to prove to the CAA!
There is no requirement for a CMR just because you have an EASA CofA.