Ed is correct in that your best option is to find a registered competent person who can do the work and notify the LABC.
There are two issues here. The first is obtaining an electrical certificate for the work and that is something any genuine electrician or company will provide for the work they do, and can also provide for existing work. Anyone *can* issue those certificates, if they have the appropriate testing equipment and the knowledge of how to use it.
The bigger issue is notification of this work to the LABC for the purposes of complying with Part P.
Registered competent persons (or companies) can ONLY notify their OWN work, so you may struggle to find one who is prepared to put their name to the work you have done, unless it is readily available for inspection and has been done exactly as that person would do.
An alternative would be to notify the LABC of your intention to do the work, pay their fee, and allow them to inspect it and certify it (which is included with their fee, whatever they tell you).
However, again that should have happened before the work started, and their attitude may or may not be cooperative at this stage of the job, especially if some of the wiring is already covered in.
Prices for installing a consumer unit will vary according to location, size of house (or more precisely, number of circuits), buggerance factor, your scheduling requirements, marketing decisions of the person or company you employ, etc, etc, so I'm afraid there is little point in giving you even a ballpark figure, though you can assume it will cost hundreds not tens of pounds.
Your best bet is to call around and get 2-3 quotes, explaining your situation, and hope you can find someone who will help you out.
You should understand that you have placed yourself in a difficult position, so be nice to anyone who comes to quote and don't complain if they are very wary about getting involved in potentially putting their name and reputation on the line for work they did not do.
On a side note, I ran into a similar situation recently which I managed to resolve with a quite nice LABC guy, but there seems to be no clear procedure in place for a situation where the work is carried out by a qualified person, who then fails to finish the job (illness, death - hopefully not by electrocution
or other acts of God).
Perhaps that is to avoid people using that excuse to try to get round the regulations, which seems to be something many people are keen to do (thats not aimed at the OP, just a general observation)