Phone your current supplier and tell them you are thinking of leaving. I have had good success at reducing costs doing this with Virgin media and Sky in the past. Last time was December last year where I got my Virgin media bill down from £79 a month to £54, but this also got me faster internet and more data on a mobile phone.
I work from home in the IT industry so a good internet connection is vital. I know I could move to a different supplier and save more, but their internet speed is nowhere near as fast as Virgin, so decided it was a case of better the devil I know for now.
Only issue is you will be locked in to a new contract for a certain period, then the price will rocket when you are out of contract, so set a reminder to tell them you want to leave and go through the game again