As I intend to put the new socket into the ring main I am imagining
that the cables will have the following routing:

Don't bother putting it on the ring properly. Run it as a spur. If the
original socket is definitely not a spur and has only two cables into it,
just run a short length of 2.5mm T&E from the existing socket to the new
one.

If the above is too complex I'll resort to disconnecting socket 1 and
connecting the exisiting wires to the new socket 2 instead. The exisiting
socket has a 70kg wardrobe in front of it so I can't get to it.

I don't get this. You need access to the socket to do your original plan
too, so you'll have to either move the wardrobe, or intercept the cable
further down the wall and install a junction box (usually in the form of an
additional double socket!) or crimps.

i.e.

new socket wanted - ****
---------------------------------------
WALL
---------------------------------------
....****......................... - ring cable
+----------+
| WARDROBE | ^
+----------+ | cut cable here to insert socket

To give:

new socket wanted - ****
----------------------.-.-------------
WALL new cable- . . - old cable, rerouted
----------------------.-.--------------
****.........****... ..........

With careful planning, it isn't necessary to extend any cables, just to add
a new section between the two new sockets. You get the bonus of an
additional double socket in the original room. This looks neater than a
junction box and requires less equipment than crimps.

Christian.