When you mean 3 core do you mean red or brown, plus black or blue, plus bare (or yellow/green sleeve)? If so this is 2 core plus earth/cpc. However if you generally mean 3 core plus earth/cpc then this is unusual - you'll need to provide more details.
The size of the cable depends on what protection it has (fuse, circuit breaker etc) and of course this needs to be in excess of the current loading required. In your case only the protection counts. Do you know what this is?
In all likelihood you need 2.5mm2/1.5mm2 twin core plus earth/cpc.
However please also consider what you are modifying. If it is a ring then one spur is OK. However if it is already a spur from a ring then it is not OK.
if you don't even have the basic knowledge of cable to use, then do you really think that you ought to be doing this?
wrong sized cabling or bad connections can and do start fires..
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