I too have issues with the iPhone 5. No case. I've never had a case. I have BT wifi the latest broadband router which is supposed to be the best.
I have to say this is the worst iPhone I've ever had. I'm currently on with my supplier of the phone as this is the second one I've had and it is still shocking. I'm currently about 4m away from the router and I have 1 bar signal.
Because of all the problems I am having with the iPhone 5 and Vodafone (call failed every other call). My supplier has given me a loan phone to see if the issues persist.
They have loaned me a Nokia Lumia. I then had them both side by side and looked at the wifi signal. My iPhone couldn't even see my wifi yet the Nokia lumina was on and connected with FULL signal.
I used to be an Apple fan but these days I am really disappointed with the product. Not to mention that using the Nokia Lumia loan phone I've not had one single "call failed" phone call
Sort it Apple!
I will have full signal showing on my screen and wi-fi will not be operational. As soon as I switch wi-fi off and go to my cell tower, voila! Perfect. Why would it be showing me full signal if there is not a full signal on the wi-fi network I have been using every day for years? I'm not sure this is the same issue as discussed in this thread, but it's the closest I can find in the forum.