You are opening a can of worms here, only a disreputable spark would sign off some one else's work.
Possibly a bit harsh and I do not want to annoy anyone who does sign off other work, but it does mean that this person would be accepting, and signing for, the design, construction and installation of your work and legally stating on certifying that the work complies with the building regulations and that it is their work.
Not many people would be prepared to risk their company and risk prosecution for this purpose.
If you have only changed a CU then you are not responsible for the installation of the rest of the circuits, though they should be safe to be reconnected.
Really if the landlord is not prepared to pay for the work to be done this is probably why he chose you as you would not insist on legal compliance and might be prepared to arrange an alternative notification, as you are now.
Overall if you felt that this was not going to be safe then you should not have taken on the job, sorry, I know it can be difficult but this is the level of responsibility you are taking on.
Have a read of this guidance from the Electrical safety Council regarding changing a CU to give you more of an idea of what you should have done.
Best practice guides : Electrical Safety Council
Guide 6 is for replacing a CU.
Regarding Building control you are now stuck since you have not complied with the prior notification requirements and there is not enough time to get registered with a scheme. Your best bet would be to try and get the landlord to agree to do the remedial works required for the safety of their tenants and consider the whole job as not completed until the rest is fixed and meanwhile arrange an assessment appointment with your chosen scheme, overall it will not cost much more registering with a scheme than notifying building control.
