There are five electrical certificates that you can get for the house. Some can be down loaded
here for free.
1) Minor Works (You will not want this one free down load)
2) Installation Certificate (You will want this and it's a free down load see above)
3) Electrical Installation Condition Report (You will not want this one it's used for existing installations again free down load)
4) Completion Certificate (This can only be issued by local authority building control and shows the work has been registered with them.)
5) Compliance Certificate (This is similar to above and issued by scheme member electricians)
To get a "Completion Certificate" you need either a Electrical Installation Certificate or a Electrical Installation Condition Report you can either have the person doing the work issue a Electrical Installation Certificate or get another electrician to issue a Electrical Installation Condition Report the former is the better approach.
For emergency work you can tell the LABC after the event but in most cases which will clearly include yours you should inform the LABC before the work starts. For a full rewire the fee is not too bad it's based on the value of work done but first band is £2000 so for small jobs it costs the same as large jobs.
The LABC can either accept the Electrical Installation Certificate issued by person doing the work or if they are not satisfied that the person is able to test their own work charge for a third party to do testing or do it them selves.
How easy to get the work passed depends on the LABC. With the work my son and I did they accepted my signature but not my sons which was a bit odd as we both had C&G 2391 and C&G 2381 (Now 2382) it seemed they did not know what they were. So it was the fact I had a degree in electronic and electrical engineering which tipped the balance and got them to accept my signature.
Insurance is again a little odd as anyone doing work should have PLI so anything resulting from work they do should in theory be claimed from their insurance not the general house insurance. However when everything went wrong with my daughter and the handy man she employed did some poor workmanship the insurance still paid for some one to come out and correct it. This sort of thing would vary between insurers but unless the inspector can clearly see the work was sub-standard likely they would pay out.
I had in my house some problems over a water leak where the inspector at first thought it was due to sub-standard work but then changed his mind.
The fact you have an installation certificate will likely show the work is not sub-standard but it also shows it should have been registered with the LABC so a double edged sword.
It is the home owner not the electrician doing the work who is responsible for notifying the council so for the electrician to complete the installation certificate does not cause him any problems. He could claim he thought you had informed the council as the council does not issue a permit to work it was at least in my case a verbal go ahead. Only reason not to issue a installation certificate is sub-standard workmanship so if he will not issue one then don't allow him to do the work.
Rewiring is not simply sticking wires in and connecting them up it does involve some planning designing and testing. To do this one needs some test equipment although those who do it on a regular basis I am sure could fudge up some results.
In 2008 the requirements changed a lot and now one has to fit RCD protection to most of the circuits which means one also has to test the RCD and the meters are not cheap. To hire around £75 for the week. So cost of meter hire needs to be included if the guy wiring does not have them.
So I expect to get all the paperwork will cost around £300 which for a £2000 job is not really that bad.