The first thing to do is correctly identify the two wires as definitely being on the same circuit. If, as it sounds, they are the two legs of a ring circuit, then you need to be sure that you have a complete ring before you proceed. To check this, turn off the power, open up a socket, disconnect all six wires, and using a continuity meter, measure between the two live wires, the two neutral wires, and then the two earth wires. The readings should be about 1Ω. The live and neutral pairs will be similar, and the two earth wires will be a fair bit higher. If you get no continuity then you have a break or you have not identified the ring.
So, you next need to decide how to connect to the ring your new sockets. If the easiest way is to connect to loose cables under the floor, then you MUST use a permanent joint. A junction box with screw-type terminals (like the brown or white round ones you get) are NOT permanent joints and shouldn't be used. Not unless the joint is permanently accessible. You need to use a joint box such as a Wago box with Wago terminals. These can be hidden under the floor. Crimps are usually acceptable but may not be suitable in this case as you can only extend cables using crimps - you can't split them.
Cut one cable, add a new single cable which goes to your new socket, and join all nine conductors in a Wago box (do this twice, for both new sockets); thus creating two spurs.
Or you can split the ring. This means that you cut one cable, extend it to a new socket, then run from that socket to a second socket, then run a return leg back to the other end of the cut cable. You will end up with twelve conductors in the junction box, joined in two sets of six conductors. This option maintains a complete ring. An advantage of splitting the ring, is that you can use crimps instead of Wago connectors. Crimps can be fitted inside a Choc-Box terminal cover box, which is very easy to fit.
If you are not confident with these type of connectors, or you would prefer to make your joint above the floor (which is recommended), then connect the new sockets directly to the existing sockets. This may require a little bit of chopping out and redecorating. The basics are still the same - either split the ring inside the socket box, or run a spur.
Remember to re-check your ring continuity before returning back on the power. This is absolutely essential as it is the only way to be sure that your cable does not become overloaded. Rings are only designed to carry 32A when they are complete.
I hope you understand the above instructions. I've written them in such a way that if you understand them, you are probably up to the job. If you have any doubts, or get strange readings, then let us know by editing your post. Or employ a registered electrician to help you out. Best of luck.