Should the rear diff on an Escort Cosworth be a LSD mine doesn't seem to be.

I've converted it to rear wheel drive and it seems to spin the inside wheel on corners not both wheels.

 

It should be, but it might just be that the diff is old and worn and it isn't working properly, as they didn't have a very high lock up rate as standard anyway. You can send it away to Bara Motorsport who would uprate your standard one, or replace it with a Titan LSD .