I know it costs about £1000 in Scotland to appeal... No idea about England but you would imagine it would be a similar fee.
EDIT:
http://playtheadvantage.com/2014/02/06/what-a-red-card-appeal-really-means-part-one/
Clubs pay for the privilege – Premier League clubs pay £1500 to lodge the claim. Lower league clubs pay progressively less. If they lose their appeal, they don’t get the fee back.