I have a room that I use as a study. It has only one single mains socket
(the other is on the opposite side of the room and would require a long
trailing cable to reach the desk area).

I currently have a PC and LCD monitor, and wall-warts for various low-power
devices (router, phone, security camera, headphones etc) plugged into a
series of multi-way socket blocks (there is a 6-way with two 4-ways plugged
into it).

Obviously the overriding factor is that the total current does not exceed 13
A, and when I measured it, it was about 3A.

But is there any safety issue with lots of plugs, via multi-way socket
blocks, all going back to a single wall socket? Is there any advantage in
having the single socket changed for a dual one and plugging half the
appliances (via socket blocks) into one socket and half into the other? Is a
single socket block with 12 sockets in any way safer than a 6-way with two
4-ways plugged into it?