I have run 2 sockets from a junction box with 2.5 cable,when I plug an appliance into one socket it works,but when I plug into the second socket both the live and nuetral become live and the appliance does not work the sockets are both the same and new

I guess you are referring to receptacles? I have no idea what "2.5" is can you please explain it to me.

If you are see zero (0) volts between white and black, make the test again and see what you have from white to ground and then from black to ground. If both are at 120 VAC (+/-) then you have a Neutral failure and it must be fixed.

Suspect that you are in the UK or EU and that you have either connected things in a series instead of parallel or that you have connected the neutral to one side of one socket and the other side in the other socket.

Are you by any chance in the UK? And do you mean a "dual socket" (one 'receptacle' with two sockets) or two separate sockets entirely?