1) If LABC are involved anyway because of "real" building work (i.e. foundations/drains/walls/windows), then AFAIK their value-based or floorspace-based fee should cover all of their responsibilities with respect to controlled work. If they don't have the expertise to inspect and test electrical work then that should be their problem, not yours, and if it were me, and they asked me for another £100-200 on top I would push back really hard.
I recently sent LABC Services (http://www.labc-services.co.uk/default.asp - an independent Building Control provider) this question:
My local Building Control dept has told me that because of staffing problems they are unable to inspect some building work, and will have to sub-contract it, and that I will therefore have to pay this cost on top of their fees.
Are they allowed to do this??
Their reply was:
Building Regulation fees are set to a scale that embraces the whole scope of what may be necessary in respect of checking and approving the plans and inspecting the work. The input necessary can vary according to the circumstances of a specific scheme, but the fees are not variable due to this feature.
The local authority has a legal duty to carry out the Building Regulation function to a proper degree. This can also vary in extent according to the demands of any scheme and considerable discretion rests with the authority. However they are responsible to give a proper service within the fee and cannot charge extra for the reason you mention. Indeed if they failed to inspect yet still charged you might have a case for a refund.
2) Electromafia-man is correct about the need to ensure that your earthing and main bonding is up to scratch, but although strongly advisable and Very Good Idea™, RCD protection for the socket circuit is not absolutely mandatory. I can't think of any good reason not to have it, only plenty of bad ones, but if for whatever reason it's not in place, and can't be sorted "in time" don't let anyone bamboozle you by erroneously "failing" the installation.