I nearly did give in during the night but I persisted! I think it helped that she put her bottle in the rubbish herself as I just kept remining her about that when she asked for a bot and she was fine. I gave her some water instead when she asked for it.
She woke up this morning with a gastro type bug so it turned out to be a good thing that she didn't have a bottle of milk in the night!
Hopefully it doesn't take too long to break the habit - I was up about 6 times in the night as she kept asking for it!