Must the sockets in a room all be on the same ring main ?

[Pobinr]

I'm re arranging the wiring in an old house. There aren't enough 13A sockets in each room. However i'm removing storage convector combi heaters from each room to be replaced with CH rads. This means there is effectively a spare ring main in the form of the ring that was used for the convector part of each heater. If I use that as another ring to give another socket in each room it means each room will have a socket on that ring & the other exisitng socket/s on the old ring. Is this OK, or must all sockets in a room be on the same ring main ?

[ElectekAir]

The only problem i see with this is if they were for storage heaters then they will only work at night time :(
If they are correctly labled then i would use the spare ring too :0