Having first had this issue on 1st November and following the tips on this thread, resorted to contacting Apple chat to see if there was any help available as battery life had now got to 3 hours on standby with no use.
Advisor suggested back up and restore, back up worked fine and then the restore froze and could not find the iphone. Advisor attempted a couple of other solutions that didn't work, I was passed to another advisor for next level technical support who advised me straight off that the phone was broken and that if I wanted it fixed it would cost me £166 !!!!
Now that phone worked, all be it with a rubbish battery life before Apple support got involved and now it is unusable and I have had to buy another (non-apple) phone.
There is clearly something going on with IOS7 that is rendering some IPhones unusable and Apple need to address this. If anyone from Apple does read this and is interested I have the case numbers to pass on.