Dzug has, as always, provided a clear and accurate answer.
As he says, a will become a public document once the grant of probate has been made. If you can't persuade the executor of the will (or his/her solicitor) to show you a copy prior to the grant being made, you can set up a 'standing search' with the Probate Registry, which means that you'll automatically be sent a copy of the will as soon as the grant is made. See here:
http://www.hmcourts-service.gov.uk/cms/1226.ht m
and here:
http://www.hmcourts-service.gov.uk/cms/1211.ht m
It only costs �5 to set up a standing search, which remains valid for up to 6 months. (If the grant of probate is not made during that period, you can renew the standing search for a further 6 months, for another �5).
Chris