I always near renewal time inform my provider that I am leaving to see what they are offering. Then the next step (as you have written down their current best offer) is to request your PUK code (i think it's called). Once this process has begun they realise you are leaving, this is the time to get in touch with the retentions department when you have seen the best deals out there.
Armed with the other competitors deals you can then barter a new contract with them, I push them as best I can till agreeing a new deal. This of course helps if you have a positive person on the other end, if you get a grumpy barsteward then say you will have a think and call back.
This works best for me and gives me a cracking tariff every time with one of the latest handsets. Good luck!