it will be easier to run new.
But remember there is no need for every socket to run up to the celing.
You bring a cable to the first socket position, then run it horizontally to the next, then the next, then the next. If it is on a ring then the last socket in the room has to go up (or down, or through the wall) to return to the CU.
When cables come down from the ceiling, it can be convenient to fit a high outlet, such as an extractor fan, near the ceiling on this drop
This is the quickest and simplest way to put sockets into a room, especially a kitchen or workshop which needs plenty. if you run the cables inside conduit or miniduct, it is very easy, at a later date, to cut into the wall and add extra sockets or switches later, without needing new chases. Oval conduit is easy to plaster over.
I recommend running your sockets all round the room. Have them at 2-metre intervals or closer. Cost and effort of additional sockets fitted at the same time is very slight.