In reply to treforsouthwell: Well yes, the French grade is for a combination of how difficult a sequence of moves are, and that can include whether they are physically difficult, technically difficult etc.
Having said that, an English 5c move is about as hard as an average 6b move. So neglecting whether or not you're mentally equipped to deal with climbing an E2, in terms of the hardest move, you should be able to climb it if you onsight 6b. So really we should be taking the technical aspect out of this.
The trouble with trad climbing is that its emotional (to a far greater extent than sport climbing for obvious reasons). So you need to remove that emotion from the equation. When I say emotion I'm talking about fear, doubt, adrenaline fuelled anxiety etc. Looking at it unemotionally it's clear that if you can climb 6b, you can climb E2 - the moves aren't any harder are they. So what's left? Controlling your head and improving your skillset so that you climb as efficiently as you can so that your brain doesn't have the leeway to screw you over and knowing what you are capable of doing.
The reality is that by and large your body is far more capable that you give it credit for. It's usually that nagging self doubt and fear creeping in which leads you to over grip, choose your gear badly or literally shut down with worry rather than you not being able to do the route. Its usually a concious (or worse sub concious) decision or set of decisions which shut you down. So try to learn to assess your climbing as you're doing it - if you feel fear, acknowledge it rather than trying to supress it. Sure you might get away with supressing it for a while but it'll get you in the end. Instead if you know its there and that eventually it will shut you down, you can do something about it - put another piece of gear in, take a rest, place a high solid piece and retreat back to somewhere that you can regroup, work out the moves, where the next rest or gear is and then launch your attack with a strategy in place. If the strategy is the wrong one, change it until it works. You see plenty of climbers (myself included) getting into something and being unwilling/unable to change their plan. Becoming more self aware is pretty important in this game and learning to play to your strengths.
All this said, climbing in our area with the exception of Cheddar is pretty steady in terms of it's steepness. It's rare that you'll find yourself unable to stand in balance on your feet. So remember that and when you feel yourself getting panicky or like you're in trouble, take a second. Breathe, look around, take time to assess your position and the holds which surround you, and the gear options which are available. Mostly there will be a way to make your situation more comfortable. Sure, you might need to move a bit but surely its better to move slightly and be comfortable rather than stay where you are and get stressed?