As Laurie says, what is your budget - both the 700D and 70-300IS are around the £350-£400, is this your maximum ? Are you wanting new or happy with 2nd hand ?
You could pick up a 40D (excellent body), 50D and probably a 60D in that price bracket. The 40D / 50D are a bigger body and a heavier camera than your 400D, so could feel better to use ? You might even be able to get a 7D (although it could be heavily used).
The 55-250IS is a great lens, especially for the cost, I've had the 70-300IS and was very happy with it, did what I wanted and I got great results with it - I only sold it to upgrade...
The 70-200F4 L is within your budget and a superb lens - it is a shorter max focal length than you currently have, but would give you excellent results and also it takes the Canon 1.4TC very well...
I suppose it depends on if you need the high FPS and do you feel the camera or the lens is restricting you...