Strictly speaking its not allowed, unless you obtain prior permission [and pay a feckin huge gratuity] from the club.
Technically the stewards can order you to wipe the contents if you have recorded any and to switch it off. They could even eject you from the stadium if you refuse.
Also, if you manage to get away with it and smuggle your video out and you then post any of it in a public place, like on a web site for instance or public broadcast, the club, the Premiership and even the FA would be able to sue you!!
All cameras including stills and recording devices like microphones are all barred under the commercial contracts the clubs and the Premiership has in place.
If you think about it, we could all go to our fav clubs, take snap shots and videos and make merchandise like calendars and posters and try to sell them etc. This is why these rules exist!
So like the guy above said, if you don't make it too obvious and don't get searched on the way in, you can probably get away with it.
Lots of people do it, you can see all the flashes going off whenever a team scores or there is a major incident at a game.
Its a bit harder to catch a guy with a flash camera that only flashes for half a second, than it is to find someone standing blatantly video-ing the match