You will be installing a sub-main from the cellar to the flat, this is a distribution circuit which you may not have come across before if your work is purely domestic.
I apologise now if I am teaching you to suck eggs here but from what you have posted so far I think this may help.
A sub main is in principle no different to a radial circuit which feeds a single point, such as an immersion heater supply or cooker supply, but usually a bit bigger.
You will need to establish how big a supply you need to the flat using diversity calculations and a bit of common sense.
You can then select a suitable sized sub-main.
I'll be surprised if you need more than 40A but personally would run a 63A supply minimum to allow for any future increase in load (eg replace gas cooker with electric)
Then you can carry out the cable size calculations as per usual.
It is advisable to use a switchfuse with bs88 fuse rather than an MCB for the OCPD.
You could use T&E cable but SWA is far more advisable, it will negate any need for an RCD on the submain. Also the cpc in large T&E will likely be too small, especially if main bonding is required. 3 core SWA will obviously give you a bonding conductor in the cable without having to run a seperate one. If no bonding requirement then 2core SWA will likely be fine.
