If you ring up and say you are thinking of leaving they will put you on to the retentions department that will offer various deals. Sadly, the lowered retention loyalty deals rarely match up to the disloyalty deals you will get from switching; especially when you take cashback offers into account as well.
I was offered around £5 a month of their listed fibre offerings. If I'd been interested in BT Sport I would probably have taken it; as I'm not I and didn't feel like subsidizing those that are and moved to PlusNet.
Recently moved from BT Infinity 2 to PlusNet. Very happy so far.