Having an additional ring in the "utility" room, which I have easier
access to wire, and where the washing machine, tumble, freezer etc are
located anyway, will enable me to run these appliances separately and
alleviate the loading problem.

Got you. I assumed that the new ring was for the kitchen, not a utility
room. It makes perfect sense to have a separate ring or radial for a utility
room.

The existing sockets in the room can either be left, or removed. I prefer to
remove sockets in these circumstances for 2 reasons. Firstly, they are
rarely in the right place or at an ideal height. Secondly, it reduces the
chance of confusion when power is cut to one circuit and not another. I have
done this in my kitchen by crimping off a couple of sockets on the existing
ring and installing the 3 new socket circuits in there.

I wouldn't install RCD protection on the utility room ring, especially if
you aren't running an extra circuit for the freezer. If the room is the
closest to the garden door, then you will need to install an RCD socket in
the box closest to the door, or an outside socket so protected positioned
such that it is unlikely that anyone would use a utility room socket for
portable outdoor appliances (which means lawnmowers and hedge trimmers).

Christian.