The IET produce two types of EIC.The long(2) and the short(1).
The long one has separate sections for designer, installer and inspector.
The people who sign these parts do not have to be the people who actually did any of the work, they do however have to be responsible for the work.
The short form is used where one person is responsible for all aspects of design, installation and inspection.
The person signing does not have to actually have carried out any of the work, just be responsible for that work.
In the OP's case there is no reason why either form cannot be used.
The only critera for filling out a certificate or PIR form is that the person be competent. There is no requirement for the person to be qualified.
The qualified person can fill out and sign the test schedule, and the OP can with a little help fill out and sign the rest of the EIC.
If the long form is used, then the person doing the I&T may be willing to sign that part of the EIC, and the OP can sign the other parts.
There is no rule or regulation stopping someone from designing their own EIC.
The DEICs that KME has refered to are probablly issued by the NICEIC.
As I understand it all of the schemes produce their own certificates, not all of them have the same information. Some require ticks in boxes to confirm tests have been done and the results are satisfactory. Others require actual readings be noted.
When I posted earlier. "The EIC can only be issued by the person conducting the installation work."
I should have been more carefull in my wording, and I apologise for not being so.