Grewcock was given the suspension last week after being found guilty of punching opposite number Thibault Privat in Bath's European Challenge Cup final defeat to Clermont Auvergne.
The ban runs from August 4 to September 15, ruling Grewcock out of England's three warm-up Tests and their first two World Cup matches, including the vital pool game with South Africa.
As a result, Grewcock was omitted from England's 47-man training squad.
England head coach Brian Ashton had little option but to omit the combative lock forward. By the time England face Samoa in their third World Cup match on September 22, Grewcock would not have played rugby for around four months.
With World Cup regulations limiting squads to just 30, Ashton could not afford to carry Grewcock in those circumstances.
But he did leave the door open and confirmed at last week's squad announcement he would revisit Grewcock's selection in the event of a successful appeal.
The independent appeal committee will be chaired by Justice Wyn Williams QC (Wales) and also comprises Mark McParland (Ireland) and Peter Brown (Scotland).