Can anyone help with advice on the ideal cable size to use please?
When you applied for Building Regulations approval, what did you say would be the way that you'd ensure that your work would comply with Part P?
Because it doesn't seem to me that someone who can't do basic cable sizing like that is likely to know all the other things which are necessary to know for safely designing, installing and testing sub-mains, consumer units and final circuits.
If you told them that the work would be done by a qualified electrician, and you then DIY it, you will find yourself horribly disappointed when they find out you misled them.
If your plan is to do it and then find an electrician to "sign it off" then you'll be able to add the disappointment of that not working to the one of LABC refusing you a completion certificate.
So depending on what you told them, and what they are expecting to happen, then it may be that the
only advice you should be given is "get an electrician".
If you are just planning to go ahead illegally, then I would strongly urge you to stop now and learn about the work you want to do before carrying on. I can guarantee that there is more to it than you think, and you cannot sensibly carry on on the basis of just asking whatever questions occur to you as you encounter things which you think you should ask about.
Below are the main points you need to cover, but you should also look at the books in the Wiki, and also start working through the online book here:
http://www.tlc-direct.co.uk/Book/1.1.htm . Unfortunately it doesn't refer to the current edition of the Wiring Regulations, but it's free, and will still give you a good grounding which you can augment with more up to date publications.