Sadly building control will not have read the EICR, or even understand how to interpret it if they did. They generally see it as the same thing as an EIC where the fact it has been issued means it has been certified as compliant.
I would imagine you could stir things up at building control by enquiring as to why they issued a completion certificate for a non-compliant installation after receiving the EICR.
Personally, and I'm sure others would agree, I think it would be a very good thing if you pressed this issue as far as possible, far too many bad installations get past building control and this needs to be brought to their attention.
As for your particular situation I would be very wary of the property, if a new installation has C2 issues in it then it is likely to have a whole host of other problems which won't/can't be seen on an EICR.
An EICR shouldn't be used to certify compliance of any new installation because you simply cannot see enough of the installation to assess it after it has been completed. An EICR is intended to check the condition of an existing installation and identify any damage, deterioration or improvements which can be made due to changes in the regulations/technology/our understanding of how to best make an installation safe.