Like most things new customers get a better incentive than existing customers
If you can be bothered with the hassle and possible down time as connection gets changed then better to move than renew contract. However if you have infinity then you need to check that cabinet is not full otherwise when you move you will lose your fibre connection and join a waiting list
No such thing as a loyal customer only a customer. BT along with most companies "bank" on "loyal" customers not moving and the vast majority of them such as your self don't because it is generally easier to stay than move.
You would need to either move to another provider and that would entail a minimum contract probably for a year or leave BT for I believe a month to be a new customer. If you do leave BT and not move to another provider you will have to pay a £30 cease charge so that might out weigh any saving you may get a a "new" customer.
Try contacting the Options Team on 0800.800.030 to negotiate a deal.
Try the Options Team again. It is not unknown for different reps to give different deals.
you can check availability here by entering your phone number http://dslchecker.bt.com/adsl/adslchecker.welcome