If the testator is alive, nobody else has the right to see his/her will. (Even those who act as witnesses are only witnessing the testator's signature. They don't have to read the contents of the will; the testator can keep them covered if he/she wishes).
If the testator has died, but a grant of probate has not yet been issued, only the executors have a right to see the contents of the will.
If probate has been granted, the will becomes a public document. Details of how you can obtain a copy can be found here:
http://www.hmcourts-service.gov.uk/cms/1226.ht m
Chris