There are some things you missed.
Firstly, the OP did ask Vivaciti the costs to move and were told it would be £8. They assumed this was the full costs and therefore didn't feel the need to look further. Vivaciti do seem to have agreed that was a mistake on their part.
There is a different between what the OP and Vivaciti have said was the offer.
The quote you give from Vivaciti suggests that the £8 + the monthly fee was all that was required. But, I think that is all that was required for the *new* line.
The OP has said they were also asked for the costs to terminate the old line (over £30 plus VAT) and that this is what they still dispute.
Vivaciti have not yet confirmed if that statement from the OP is correct or whether the offer you quoted was the complete total for old and new line costs combined.