Again a lot of guess work. But I will guess it was intended to have ceiling roses and once the ceiling rose is fitted you can then also have light switches controlling each lamp.
A ceiling rose has normally three cables, one brings power to the rose, one takes power to next rose, and one connects rose to the light switch. That last cable is it seems as yet unused, to use this cable you need some brown sleeving as the blue wire is used as line so needs sleeving to show that. So at the moment the switch wires are unused so you should be able to identify them reasonably easy.
The ceiling rose has 4 connections an earth clamp and then a row with two, three, and three hole connectors, Centre three are permanent line, where the outer double is switched line and outer triple is neutral. So as the ceiling roses are fitted the switches will start to work.
The board also shows two 16A MCB's connected so you do not have a dead flat something is connected.
Electrics are often done in two stages, first and second fix, it would seem the electrician has done the first fix, now you need some one to do the second fix, where the problem arises is at the first fix stage no paperwork needs raising so any new electrician has no idea as what was planed. Some things become obvious but it is easy to make a mistake. I remember many years ago taking over a job and found after fitting all sockets I did not have a ring circuit some where the plaster had plastered over a socket box now I had to find it. With sockets no so bad but with radial circuits it is so easy to make a cable live which is not connected to any item. So in theroy only guy who can second fix is the one who started the job.
In my case first fix was done by an electrician employed by the same firm and a few phone calls could work out what was there and there was no real option I did not really have the option of telling my boss no I am not second fixing some one else's work. However in your case you are trying to find an electrician willing to take over the job. Normally this will be day rate, i.e. open cheque book, as the electrician has no idea what he may find. And at the end he has to sign to say he has done the work. This is a problem.
There are two forms, one which is normally used with domestic has just one signature, the other has three signatures, the latter is split into design, installation and lastly inspection and testing. The new electrician has not done the design, and only done part of the installation, so in real terms should only be signing the inspection and testing. To get a compliance certificate he must sign for all three, he may get a completion certificate only signing for the last stage I have submitted certificates to the LABC clearly marked as to the limitations to my work and they have issued a completion certificate. Personally I think the LABC inspector was taking quite a chance, but he did issue it.
In theroy the electrician taking over the job needs to re-do the work, if he can see the routes of all cables then he can sign but the whole idea of first and second fix is that the cables are covered between the two stages. So you are at the whim of the new electrician, he and only he can say I am happy with that I don't need assess, or I want to remove that plaster I think there may be a problem. This is why he is paid day rate not a fee for the whole job.
For the last job I took over it was my mothers house and I had seen what the electrician was doing so I was both happy, and had no option but take over the job. As to taking over the job the first thing I did which in hind sight may have been a mistake was to contact the LABC and tell them I was taking over the work. As luck has it because it was for the disabled there was no charge, other wise it would have cost me around £200 to involve the LABC and once they are told you can't really untell them. I had two advantages over you, one I am an electrician, and two I had the test gear required. The latter is really important.
Test gear required will cost around £750 to buy or £75 to rent for a week which is normally shortest rental time as they need re-calibrating after each rental, using the test gear can be dangerous is not done correctly, for an electrician the course to train how to inspect and test is 3 hours a week for 12 weeks to give you some idea what is involved, the exam gets around a 75% pass rate and this is for electricians.
To work on an owner occupied house or flat although the standards should be the same one can get away with items which would end you up in court if the property was rented. i.e. in my own house if a socket is smashed I would just replace it, in some one else's house I would also test it to ensure the loop impedance, and RCD tripping times were within the limits. I should test my own house, but I know it's OK as I retest sockets many times to ensure my meters have not gone out so I know they are OK. When testing other peoples houses I so often high light faults I would not dream of not testing.